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Journal articles on the topic 'Quaziregular degenerate differential equation'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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1

Bass, Richard F., Krzysztof Burdzy, and Zhen-Qing Chen. "Pathwise uniqueness for a degenerate stochastic differential equation." Annals of Probability 35, no. 6 (2007): 2385–418. http://dx.doi.org/10.1214/009117907000000033.

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2

Cao, Hai Tao, and Xing Ye Yue. "Homogenization of a nonlinear degenerate parabolic differential equation." Acta Mathematica Sinica, English Series 29, no. 7 (2013): 1429–36. http://dx.doi.org/10.1007/s10114-013-2133-0.

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3

Pyo, Sung-Soo, Taekyun Kim, and Seog-Hoon Rim. "Degenerate Daehee Numbers of the Third Kind." Mathematics 6, no. 11 (2018): 239. http://dx.doi.org/10.3390/math6110239.

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In this paper, we define new Daehee numbers, the degenerate Daehee numbers of the third kind, using the degenerate log function as generating function. We obtain some identities for the degenerate Daehee numbers of the third kind associated with the Daehee, degenerate Daehee, and degenerate Daehee numbers of the second kind. In addition, we derive a differential equation associated with the degenerate log function. We deduce some identities from the differential equation.

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4

Wong, M. W. "Weyl transforms and a degenerate elliptic partial differential equation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2064 (2005): 3863–70. http://dx.doi.org/10.1098/rspa.2005.1560.

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We give a formula for the inverse of a degenerate elliptic partial differential operator P on related to the Heisenberg group. The formula is in terms of pseudo-differential operators of the Weyl type, i.e. Weyl transforms. The technique is to use the Fourier–Wigner transforms of Hermite functions, which form an orthonormal basis for . Using the formula for the inverse, we give an estimate for the L p norm of the solution u of the partial differential equation Pu = f on in terms of the L 2 norm of f , 2≤ p ≤∞.

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5

Akhtyamov, A. M. "Degenerate Boundary Conditions for a Third-Order Differential Equation." Differential Equations 54, no. 4 (2018): 419–26. http://dx.doi.org/10.1134/s0012266118040018.

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6

Macionis, J. "Solvability of a degenerate differential equation with spectral parameter." Lithuanian Mathematical Journal 25, no. 2 (1986): 162–65. http://dx.doi.org/10.1007/bf00966182.

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7

Rutkas, A. G., and I. G. Khudoshin. "Global solvability of one degenerate semilinear differential operator equation." Nonlinear Oscillations 7, no. 3 (2004): 403–17. http://dx.doi.org/10.1007/s11072-005-0020-z.

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8

Bandaliyev, R. A., I. G. Mamedov, A. B. Abdullayeva, and K. H. Safarova. "Optimal Control Problem for a Degenerate Fractional Differential Equation." Lobachevskii Journal of Mathematics 42, no. 6 (2021): 1239–47. http://dx.doi.org/10.1134/s1995080221060056.

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9

Amar, Micol, Daniele Andreucci, Roberto Gianni, and Claudia Timofte. "A degenerate pseudo-parabolic equation with memory." Communications in Applied and Industrial Mathematics 10, no. 1 (2019): 71–77. http://dx.doi.org/10.2478/caim-2019-0013.

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Abstract We prove the existence and uniqueness for a degenerate pseudo-parabolic problem with memory. This kind of problem arises in the study of the homogenization of some differential systems involving the Laplace-Beltrami operator and describes the effective behaviour of the electrical conduction in some composite materials.

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10

Tepoyan, L. P. "DEGENERATE FIRST ORDER DIFFERENTIAL-OPERATOR EQUATIONS." Proceedings of the YSU A: Physical and Mathematical Sciences 53, no. 3 (250) (2019): 163–69. http://dx.doi.org/10.46991/pysu:a/2019.53.3.163.

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We consider boundary value problem for degenerate first order differentialoperator equation $Lu \mathclose{\equiv} t^{\alpha} u^{\prime} \mathclose{-} P u \mathclose{=} f $, $ u(0) \mathclose{-} \mu u(b) \mathclose{=} 0 $, where $ t \mathclose{\in} (0,b) $, $ a \mathclose{\geq} 0 $, $ P: H \mathclose{\rightarrow} H $ is linear operator in separable Hilbert space $ H $, $ f \mathclose{\in} L_{2, \beta} ((0,b),H) $, $ \mu \mathclose{\in} \mathbb{C} $. We prove that under some conditions on the operator $ P $ and number $ \mu $ the boundary value problem has unique generalized solution $ u \mathc

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11

Vlasenko, L. A., and A. G. Rutkas. "Uniqueness and approximation theorems for a degenerate operator-differential equation." Mathematical Notes 60, no. 4 (1996): 445–49. http://dx.doi.org/10.1007/bf02305428.

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12

Yuldashev, T. K. "Mixed problem for pseudoparabolic integro-differential equation with degenerate kernel." Differential Equations 53, no. 1 (2017): 99–108. http://dx.doi.org/10.1134/s0012266117010098.

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13

El-Fiky, Ahmed. "On the Cauchy problem for a degenerate parabolic differential equation." International Journal of Mathematics and Mathematical Sciences 21, no. 3 (1998): 555–58. http://dx.doi.org/10.1155/s0161171298000763.

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14

Bhattacharya, Tilak, and Leonardo Marazzi. "On the viscosity solutions to a degenerate parabolic differential equation." Annali di Matematica Pura ed Applicata (1923 -) 194, no. 5 (2014): 1423–54. http://dx.doi.org/10.1007/s10231-014-0427-1.

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15

Christodoulou, Dimitris M., Eric Kehoe, and Qutaibeh D. Katatbeh. "Degenerate Canonical Forms of Ordinary Second-Order Linear Homogeneous Differential Equations." Axioms 10, no. 2 (2021): 94. http://dx.doi.org/10.3390/axioms10020094.

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For each fundamental and widely used ordinary second-order linear homogeneous differential equation of mathematical physics, we derive a family of associated differential equations that share the same “degenerate” canonical form. These equations can be solved easily if the original equation is known to possess analytic solutions, otherwise their properties and the properties of their solutions are de facto known as they are comparable to those already deduced for the fundamental equation. We analyze several particular cases of new families related to some of the famous differential equations a

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16

Ding, Da-Jiang, Di-Qing Jin, and Chao-Qing Dai. "Analytical solutions of differential-difference sine-Gordon equation." Thermal Science 21, no. 4 (2017): 1701–5. http://dx.doi.org/10.2298/tsci160809056d.

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In modern textile engineering, non-linear differential-difference equations are often used to describe some phenomena arising in heat/electron conduction and flow in carbon nanotubes. In this paper, we extend the variable coefficient Jacobian elliptic function method to solve non-linear differential-difference sine-Gordon equation by introducing a negative power and some variable coefficients in the ansatz, and derive two series of Jacobian elliptic function solutions. When the modulus of Jacobian elliptic function approaches to 1, some solutions can degenerate into some known solutions in the

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17

Yuldashev, T. K., and J. A. Artykova. "Initial problem for a nonlinear integro-differential equation with a higher-order hyperbolic operator and with reflection of the argument." Daghestan Electronic Mathematical Reports, no. 13 (2020): 31–56. http://dx.doi.org/10.31029/demr.13.3.

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In this paper it is studied the questions of one value solvability of initial value problem for nonlinear integro-differential equation with hyperbolic operator of the higher order, with degenerate kernel and reflective argument for regular values of spectral parameter. It is expressed the partial differential operator on the left-hand side of equation of higher order by the superposition of first-order partial differential operators. This is allowed us to present the considering integro-differential equation as an integral equation, describing the change of the unknown function along the char

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18

Hwang, Kyung-Won, Young-Soo Seol, and Cheon-Seoung Ryoo. "Explicit Identities for 3-Variable Degenerate Hermite Kampé de Fériet Polynomials and Differential Equation Derived from Generating Function." Symmetry 13, no. 1 (2020): 7. http://dx.doi.org/10.3390/sym13010007.

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We get the 3-variable degenerate Hermite Kampé de Fériet polynomials and get symmetric identities for 3-variable degenerate Hermite Kampé de Fériet polynomials. We make differential equations coming from the generating functions of degenerate Hermite Kampé de Fériet polynomials to get some identities for 3-variable degenerate Hermite Kampé de Fériet polynomials,. Finally, we study the structure and symmetry of pattern about the zeros of the 3-variable degenerate Hermite Kampé de Fériet equations.

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19

CAI, Gang. "Periodic solution of second order degenerate differential equation in Banach spaces." SCIENTIA SINICA Mathematica 45, no. 4 (2015): 381–92. http://dx.doi.org/10.1360/012015-16.

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20

Kvedaras, B. "The structure of a strongly degenerate differential equation with holomorphic coefficients." Lithuanian Mathematical Journal 36, no. 2 (1996): 131–41. http://dx.doi.org/10.1007/bf02986895.

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21

Bu, Shangquan, and Gang Cai. "Well-posedness of fractional degenerate differential equations in Banach spaces." Fractional Calculus and Applied Analysis 22, no. 2 (2019): 379–95. http://dx.doi.org/10.1515/fca-2019-0023.

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Abstract We study the well-posedness of the fractional degenerate differential equation: Dα (Mu)(t) + cDβ(Mu)(t) = Au(t) + f(t), (0 ≤ t ≤ 2π) on Lebesgue-Bochner spaces Lp(𝕋; X) and periodic Besov spaces $\begin{array}{} B_{p,q}^s \end{array}$ (𝕋; X), where A and M are closed linear operators in a complex Banach space X satisfying D(A) ⊂ D(M), c ∈ ℂ and 0 < β < α are fixed. Using known operator-valued Fourier multiplier theorems, we give necessary and sufficient conditions for Lp-well-posedness and $\begin{array}{} B_{p,q}^s \end{array}$-well-posedness of above equation.

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22

Mohammed, Ahmed. "Hölder continuity of solutions of some degenerate elliptic differential equations." Bulletin of the Australian Mathematical Society 62, no. 3 (2000): 369–77. http://dx.doi.org/10.1017/s0004972700018888.

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23

Tepoyan, L. "DEGENERATE DIFFERENTIAL-OPERATOR EQUATIONS OF HIGHER ORDER AND ARBITRARY WEIGHT." Asian-European Journal of Mathematics 05, no. 02 (2012): 1250030. http://dx.doi.org/10.1142/s1793557112500301.

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We consider the Dirichlet problem for a degenerate differential-operator equation of higher order with arbitrary weight-function ρ(t). We establish some embedding and compactness theorems in weighted Sobolev spaces, show existence and uniqueness of the generalized solutions. We also give a description of the spectrum for the corresponding operator.

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24

Hairer, M. "Exponential mixing for a stochastic partial differential equation driven by degenerate noise." Nonlinearity 15, no. 2 (2002): 271–79. http://dx.doi.org/10.1088/0951-7715/15/2/304.

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25

Yuldashev, T. K. "ON AN INTEGRO-DIFFERENTIAL EQUATION OF PSEUDOPARABOLIC-PSEUDOHYPERBOLIC TYPE WITH DEGENERATE KERNELS." Proceedings of the YSU A: Physical and Mathematical Sciences 52, no. 1 (245) (2018): 19–26. http://dx.doi.org/10.46991/pysu:a/2018.52.1.019.

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In the article the questions of solvability of boundary value problem for a homogeneous pseudoparabolic-pseudohyperbolic type integro-differential equation with degenerate kernels are considered. The Fourier method based on separation of variables is used. A criterion for the one-valued solvability of the considering problem is found. Under this criterion the one-valued solvability of the problem is proved.

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26

Macionis, J. "Boundedness of the solution of a degenerate second order differential equation system." Lithuanian Mathematical Journal 36, no. 1 (1995): 79–83. http://dx.doi.org/10.1007/bf02337051.

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27

Macionis, J. "Boundedness of the solution of a degenerate second order differential equation system." Lithuanian Mathematical Journal 35, no. 1 (1995): 79–83. http://dx.doi.org/10.1007/bf02337757.

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28

Nurgabyl, D. N., and S. S. Nazhim. "Recovery problem for a singularly perturbed differential equation with an initial jump." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 100, no. 4 (2020): 125–35. http://dx.doi.org/10.31489/2020m4/125-135.

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The article investigates the asymptotic behavior of the solution to reconstructing the boundary conditions and the right-hand side for second-order differential equations with a small parameter at the highest derivative, which have an initial jump. Asymptotic estimates of the solution of the reconstruction problem are obtained for singularly perturbed second-order equations with an initial jump. The rules for the restoration of boundary conditions and the right parts of the original and degenerate problems are established. The asymptotic estimates of the solution of the perturbed problem are d

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29

Akhtyamov, A. M. "Survey of studies on degenerate boundary conditions and finite spectrum." Multiphase Systems 14, no. 3 (2019): 184–201. http://dx.doi.org/10.21662/mfs2019.3.025.

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It is shown that for the asymmetric diffusion operator the case when the characteristic determinant is identically equal to zero is impossible and the only possible degenerate boundary conditions are the Cauchy conditions. In the case of a symmetric diffusion operator, the characteristic determinant is identically equal to zero if and only if the boundary conditions are false–periodic boundary conditions and is identically equal to a constant other than zero if and only if its boundary conditions are generalized Cauchy conditions. All degenerate boundary conditions for a spectral problem with

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30

Zhan, Huashui. "On the Weak Characteristic Function Method for a Degenerate Parabolic Equation." Journal of Function Spaces 2019 (August 26, 2019): 1–11. http://dx.doi.org/10.1155/2019/9040284.

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For a nonlinear degenerate parabolic equation, how to impose a suitable boundary value condition to ensure the well-posedness of weak solutions is a very important problem. It is well known that the classical Fichera-Oleinik theory has perfectly solved the problem for the linear case, and the optimal boundary value condition matching up with a linear degenerate parabolic equation can be depicted out by Fechira function. In this paper, a new method, which is called the weak characteristic function method, is introduced. By this new method, the partial boundary condition matching up with a nonli

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31

BARUCCI, E., S. POLIDORO, and V. VESPRI. "SOME RESULTS ON PARTIAL DIFFERENTIAL EQUATIONS AND ASIAN OPTIONS." Mathematical Models and Methods in Applied Sciences 11, no. 03 (2001): 475–97. http://dx.doi.org/10.1142/s0218202501000945.

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We analyze partial differential equations arising in the evaluation of Asian options. The equations are strongly degenerate partial differential equations in three dimensions. We show that the solution of the no-arbitrage partial differential equation is sufficiently regular and standard numerical methods can be employed to approximate it.

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32

BARILLON, C., G. M. MAKHVILADZE, and V. VOLPERT. "Stability of stationary solutions for a degenerate parabolic system." European Journal of Applied Mathematics 12, no. 1 (2001): 57–75. http://dx.doi.org/10.1017/s0956792501004430.

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The paper is devoted to the stability of stationary solutions of an evolution system, describing heat explosion in a two-phase medium, where a parabolic equation is coupled with an ordinary differential equation. Spectral properties of the problem linearized about a stationary solution are analyzed and used to study stability of continuous branches of solutions. For the convex nonlinearity specific to combustion problems it is shown that solutions on the first increasing branch are stable, solutions on all other branches are unstable. These results remain valid for the scalar equation and they

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33

Fomin, V. I. "On a Weakly Degenerate First-Order Linear Differential Equation in a Banach Space." Differential Equations 41, no. 10 (2005): 1514–16. http://dx.doi.org/10.1007/s10625-005-0309-9.

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34

Baten, Azizul, and Anton Abdulbasah Kamil. "Optimal Production Control in Stochastic Manufacturing Systems with Degenerate Demand." East Asian Journal on Applied Mathematics 1, no. 1 (2011): 89–96. http://dx.doi.org/10.4208/eajam.190609.190510a.

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AbstractThe paper studies the production inventory problem of minimizing the expected discounted present value of production cost control in manufacturing systems with degenerate stochastic demand. We have developed the optimal inventory production control problem by deriving the dynamics of the inventory-demand ratio that evolves according to a stochastic neoclassical differential equation through Ito's Lemma. We have also established the Riccati based solution of the reduced (one- dimensional) HJB equation corresponding to production inventory control problem through the technique of dynamic

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35

Qiu, Wenhua, and Jianguo Si. "Reducibility for a Class of Almost-Periodic Differential Equations with Degenerate Equilibrium Point under Small Almost-Periodic Perturbations." Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/386812.

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This paper focuses on almost-periodic time-dependent perturbations of an almost-periodic differential equation near the degenerate equilibrium point. Using the KAM method, the perturbed equation can be reduced to a suitable normal form with zero as equilibrium point by an affine almost-periodic transformation. Hence, for the equation we can obtain a small almost-periodic solution.

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36

Cai, Xin. "Effective Approximation for Elliptic Partial Differential Equation with Periodical Boundary Value Problem." Applied Mechanics and Materials 29-32 (August 2010): 1294–300. http://dx.doi.org/10.4028/www.scientific.net/amm.29-32.1294.

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Elliptic partial differential equation with periodical boundary value problem was considered. The equation would degenerate to parabolic partial differential equation when small parameter tends to zero. This is a multi-scale problem. Firstly, the property of boundary layer was discussed. Secondly, the boundary layer function was presented. The smooth component was constructed according to the boundary layer function. Thirdly, finite difference scheme for the smooth component is proposed according to transition point in time direction. Finally, experiment was proposed to illustrate that our pre

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37

Plekhanova, Marina, and Guzel Baybulatova. "Multi-Term Fractional Degenerate Evolution Equations and Optimal Control Problems." Mathematics 8, no. 4 (2020): 483. http://dx.doi.org/10.3390/math8040483.

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A theorem on unique solvability in the sense of the strong solutions is proved for a class of degenerate multi-term fractional equations in Banach spaces. It applies to the deriving of the conditions on unique solution existence for an optimal control problem to the corresponding equation. Obtained results are used to an optimal control problem study for a model system which is described by an initial-boundary value problem for a partial differential equation.

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38

Sarıaydın-Filibelioğlu, Ayşe, Bülent Karasözen, and Murat Uzunca. "Energy Stable Interior Penalty Discontinuous Galerkin Finite Element Method for Cahn–Hilliard Equation." International Journal of Nonlinear Sciences and Numerical Simulation 18, no. 5 (2017): 303–14. http://dx.doi.org/10.1515/ijnsns-2016-0024.

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AbstractAn energy stable conservative method is developed for the Cahn–Hilliard (CH) equation with the degenerate mobility. The CH equation is discretized in space with the mass conserving symmetric interior penalty discontinuous Galerkin (SIPG) method. The resulting semi-discrete nonlinear system of ordinary differential equations are solved in time by the unconditionally energy stable average vector field (AVF) method. We prove that the AVF method preserves the energy decreasing property of the fully discretized CH equation. Numerical results for the quartic double-well and the logarithmic p

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39

Kombe, Ismail. "Cauchy-Dirichlet problem for the nonlinear degenerate parabolic equations." Abstract and Applied Analysis 2005, no. 6 (2005): 607–17. http://dx.doi.org/10.1155/aaa.2005.607.

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We will investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation:∂u/∂t=ℒu+V(w)up−1inΩ×(0,T),1<p<2,u(w,0)=u0(w)≥0inΩ,u(w,t)=0on∂Ω×(0,T)whereℒis the subellipticp-Laplacian andV∈Lloc1(Ω).

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40

Yuldashev, T. K., and E. T. Karimov. "Mixed type integro-differential equation with fractional order Caputo operators and spectral parameters." Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta 57 (May 2021): 190–205. http://dx.doi.org/10.35634/2226-3594-2021-57-10.

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The issues of unique solvability of a boundary value problem for a mixed type integro-differential equation with two Caputo time-fractional operators and spectral parameters are considered. A mixed type integro-differential equation is a partial integro-differential equation of fractional order in both positive and negative parts of multidimensional rectangular domain under consideration. The fractional Caputo operator's order is less in the positive part of the domain, than the order of Caputo operator in the negative part of the domain. Using the method of Fourier series, two systems of coun

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41

Baleanu, Dumitru, Vladimir E. Fedorov, Dmitriy M. Gordievskikh, and Kenan Taş. "Approximate Controllability of Infinite-Dimensional Degenerate Fractional Order Systems in the Sectorial Case." Mathematics 7, no. 8 (2019): 735. http://dx.doi.org/10.3390/math7080735.

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We consider a class of linear inhomogeneous equations in a Banach space not solvable with respect to the fractional Caputo derivative. Such equations are called degenerate. We study the case of the existence of a resolving operators family for the respective homogeneous equation, which is an analytic in a sector. The existence of a unique solution of the Cauchy problem and of the Showalter—Sidorov problem to the inhomogeneous degenerate equation is proved. We also derive the form of the solution. The approximate controllability of infinite-dimensional control systems, described by the equation

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42

Yan, Baisheng. "On stability and asymptotic behaviours for a degenerate Landau–Lifshitz equation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 145, no. 3 (2015): 657–68. http://dx.doi.org/10.1017/s0308210513001406.

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In this paper we study the problem concerning stability and asymptotic behaviours of solutions for a degenerate Landau–Lifshitz equation in micromagnetics involving only the non-local magnetostatic energy. Due to the lack of derivative estimates, we do not have the compactness needed for strong convergence and the natural convergence is weak* convergence. By formulating the problem in a new framework of differential inclusions, we show that the Cauchy problems for such an equation are not stable under the weak* convergence of initial data. For the asymptotic behaviours of weak solutions, we es

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43

Yuldashev, T. K. "Nonlocal Boundary Value Problem for a Nonlinear Fredholm Integro-Differential Equation with Degenerate Kernel." Differential Equations 54, no. 12 (2018): 1646–53. http://dx.doi.org/10.1134/s0012266118120108.

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44

Akimenko, V. V., A. G. Nakonechnyi, and O. Yu Trofimchuka. "Modeling convection–diffusion processes based on a multidimensional integro-differential equation with degenerate parabolicity." Cybernetics and Systems Analysis 45, no. 2 (2009): 232–44. http://dx.doi.org/10.1007/s10559-009-9087-3.

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45

Yuldashev, T. K. "Inverse Boundary-Value Problem for an Integro-Differential Boussinesq-Type Equation with Degenerate Kernel." Journal of Mathematical Sciences 250, no. 5 (2020): 847–58. http://dx.doi.org/10.1007/s10958-020-05050-2.

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46

Kvedaras, B. "Representation of solutions of a strongly degenerate second-order differential equation in Hilbert space." Lithuanian Mathematical Journal 27, no. 1 (1987): 41–46. http://dx.doi.org/10.1007/bf00972020.

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47

Yuldashev, T. K., Yu P. Apakov, and A. Kh Zhuraev. "Boundary Value Problem for Third Order Partial Integro-Differential Equation with a Degenerate Kernel." Lobachevskii Journal of Mathematics 42, no. 6 (2021): 1317–27. http://dx.doi.org/10.1134/s1995080221060329.

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48

XU, JUNXIANG, and SHUNJUN JIANG. "Reducibility for a class of nonlinear quasi-periodic differential equations with degenerate equilibrium point under small perturbation." Ergodic Theory and Dynamical Systems 31, no. 2 (2010): 599–611. http://dx.doi.org/10.1017/s0143385709001114.

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AbstractIn this paper, using the Kolmogorov–Arnold–Moser method we prove reducibility of a class of nonlinear quasi-periodic differential equation with degenerate equilibrium point under small perturbation and obtain a quasi-periodic solution near the equilibrium point.

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49

Fedorov, Vladimir E., and Roman R. Nazhimov. "Inverse problems for a class of degenerate evolution equations with Riemann – Liouville derivative." Fractional Calculus and Applied Analysis 22, no. 2 (2019): 271–86. http://dx.doi.org/10.1515/fca-2019-0018.

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Abstract Unique solvability and well-posedness issues are studied for linear inverse problems with a constant unknown parameter to fractional order differential equations with Riemann – Liouvlle derivative in Banach spaces. Firstly, well-posedness criteria for the inverse problem with the Cauchy type initial conditions to the differential equation in a Banach space that solved with respect to the fractional derivative is obtained. This result is applied to search of sufficient conditions for the unique solution existence of the inverse problem for equation with linear degenerate operator at th

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50

Cavalheiro, Albo Carlos. "Solvability of nonlinear Dirichlet problem for a class of degenerate elliptic equations." Abstract and Applied Analysis 2004, no. 3 (2004): 205–14. http://dx.doi.org/10.1155/s1085337504310043.

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We prove an existence result for solution to a class of nonlinear degenerate elliptic equation associated with a class of partial differential operators of the formLu(x)=∑i,j=1nDj(aij(x)Diu(x)), withDj=∂/∂xj, whereaij:Ω→ℝare functionssatisfying suitable hypotheses.

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