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Journal articles on the topic 'Nonlinear Potential Theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Kuusi, Tuomo, and Giuseppe Mingione. "Linear Potentials in Nonlinear Potential Theory." Archive for Rational Mechanics and Analysis 207, no. 1 (August 29, 2012): 215–46. http://dx.doi.org/10.1007/s00205-012-0562-z.

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2

Kuusi, Tuomo, and Giuseppe Mingione. "Vectorial nonlinear potential theory." Journal of the European Mathematical Society 20, no. 4 (February 28, 2018): 929–1004. http://dx.doi.org/10.4171/jems/780.

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3

Adams, David R. "Weighted nonlinear potential theory." Transactions of the American Mathematical Society 297, no. 1 (January 1, 1986): 73. http://dx.doi.org/10.1090/s0002-9947-1986-0849468-4.

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4

Kilpel�inen, Tero. "Nonlinear potential theory and PDEs." Potential Analysis 3, no. 1 (March 1994): 107–18. http://dx.doi.org/10.1007/bf01047838.

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5

Heinonen, J., T. Kilpeläinen, and O. Martio. "Harmonic morphisms in nonlinear potential theory." Nagoya Mathematical Journal 125 (March 1992): 115–40. http://dx.doi.org/10.1017/s0027763000003937.

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This article concerns the following problem: given a family of partial differential operators with similar structure and given a continuous mapping f from an open set Ω in Rn into Rn, then when does f pull back the solutions of one equation in the family to solutions of another equation in that family? This problem is typical in the theory of differential equations when one wants to use a coordinate change to study solutions in a different environment.

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6

Kuusi, Tuomo, and Giuseppe Mingione. "Nonlinear Potential Theory of elliptic systems." Nonlinear Analysis 138 (June 2016): 277–99. http://dx.doi.org/10.1016/j.na.2015.12.022.

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7

Kinnunen, Juha, and Olli Martio. "Nonlinear potential theory on metric spaces." Illinois Journal of Mathematics 46, no. 3 (July 2002): 857–83. http://dx.doi.org/10.1215/ijm/1258130989.

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8

Björn, Anders. "Weak Barriers in Nonlinear Potential Theory." Potential Analysis 27, no. 4 (October 9, 2007): 381–87. http://dx.doi.org/10.1007/s11118-007-9064-2.

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9

Mingione, Giuseppe, and Giampiero Palatucci. "Developments and perspectives in Nonlinear Potential Theory." Nonlinear Analysis 194 (May 2020): 111452. http://dx.doi.org/10.1016/j.na.2019.02.006.

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10

Aïssaoui, Noureddine. "Strongly nonlinear potential theory on metric spaces." Abstract and Applied Analysis 7, no. 7 (2002): 357–74. http://dx.doi.org/10.1155/s1085337502203024.

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We define Orlicz-Sobolev spaces on an arbitrary metric space with a Borel regular outer measure, and we develop a capacity theory based on these spaces. We study basic properties of capacity and several convergence results. We prove that each Orlicz-Sobolev function has a quasi-continuous representative. We give estimates for the capacity of balls when the measure is doubling. Under additional regularity assumption on the measure, we establish some relations between capacity and Hausdorff measures.

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11

Kilpeläinen, Tero, and Jan Malý. "Generalized dirichlet problem in nonlinear potential theory." Manuscripta Mathematica 66, no. 1 (December 1990): 25–44. http://dx.doi.org/10.1007/bf02568480.

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12

Maeda, Fumi-Yuki, and Takayori Ono. "Properties of harmonic boundary in nonlinear potential theory." Hiroshima Mathematical Journal 30, no. 3 (2000): 513–23. http://dx.doi.org/10.32917/hmj/1206124611.

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13

Adams, David R., and John L. Lewis. "Fine and quasi connectedness in nonlinear potential theory." Annales de l’institut Fourier 35, no. 1 (1985): 57–73. http://dx.doi.org/10.5802/aif.998.

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14

Holopainen, Ilkka, and Seppo Rickman. "Classification of Riemannian manifolds in nonlinear potential theory." Potential Analysis 2, no. 1 (March 1993): 37–66. http://dx.doi.org/10.1007/bf01047672.

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15

Rao, Murali, and Zoran Vondraćek. "Nonlinear potentials in function spaces." Nagoya Mathematical Journal 165 (March 2002): 91–116. http://dx.doi.org/10.1017/s0027763000008163.

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We introduce a framework for a nonlinear potential theory without a kernel on a reflexive, strictly convex and smooth Banach space of functions. Nonlinear potentials are defined as images of nonnegative continuous linear functionals on that space under the duality mapping. We study potentials and reduced functions by using a variant of the Gauss-Frostman quadratic functional. The framework allows a development of other main concepts of nonlinear potential theory such as capacities, equilibrium potentials and measures of finite energy.

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16

Idiart, Martín I., and Pedro Ponte Castañeda. "Field statistics in nonlinear composites. I. Theory." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2077 (August 22, 2006): 183–202. http://dx.doi.org/10.1098/rspa.2006.1756.

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This work presents a means for extracting the statistics of the local fields in nonlinear composites from the effective potential of suitably perturbed composites. The idea is to introduce a parameter in the local potentials, generally a tensor, such that differentiation of the corresponding effective potential with respect to the parameter yields the volume average of the desired quantity. In particular, this provides a generalization to the nonlinear case of well-known formulas in the context of linear composites, which express phase averages and second moments of the local fields in terms of derivatives of the effective potential. Such expressions are useful since they allow the generation of estimates for the field statistics in nonlinear composites, directly from homogenization estimates for appropriately defined effective potentials. Here, use is made of these expressions in the context of the ‘variational’, ‘tangent second-order’ and ‘second-order’ homogenization methods, to obtain rigorous estimates for the first and second moments of the fields in nonlinear composites. While the variational estimates for these quantities are found to be identical to those proposed in previous works, the tangent second-order and second-order estimates are found be different. In particular, the new estimates for the first moments given in this work are found to be entirely consistent with the corresponding estimates for the macroscopic behaviour. Sample results for two-phase, power-law composites are provided in part II of this work.

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17

Garofalo, Nicola. "Book Review: Nonlinear potential theory of degenerate elliptic equations." Bulletin of the American Mathematical Society 31, no. 2 (October 1, 1994): 318–28. http://dx.doi.org/10.1090/s0273-0979-1994-00543-9.

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18

Vodop’yanov, S. K., and N. A. Kudryavtseva. "Nonlinear potential theory for Sobolev spaces on Carnot groups." Siberian Mathematical Journal 50, no. 5 (September 2009): 803–19. http://dx.doi.org/10.1007/s11202-009-0091-7.

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19

Bondar', V. D. "Complex-potential method in the nonlinear theory of elasticity." Journal of Applied Mechanics and Technical Physics 41, no. 1 (January 2000): 120–30. http://dx.doi.org/10.1007/bf02465246.

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20

Hayashi, Masayuki. "Potential well theory for the derivative nonlinear Schrödinger equation." Analysis & PDE 14, no. 3 (May 18, 2021): 909–44. http://dx.doi.org/10.2140/apde.2021.14.909.

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21

Kim, Yong Jung, and Robert J. McCann. "Potential theory and optimal convergence rates in fast nonlinear diffusion." Journal de Mathématiques Pures et Appliquées 86, no. 1 (July 2006): 42–67. http://dx.doi.org/10.1016/j.matpur.2006.01.002.

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22

Nakai, Mitsuru. "Existence of dirichlet finite harmonic measures in nonlinear potential theory." Complex Variables, Theory and Application: An International Journal 21, no. 1-2 (February 1993): 107–14. http://dx.doi.org/10.1080/17476939308814619.

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23

Wegert, Elias. "On a nonlinear problem of the theory of potential flows." Quarterly of Applied Mathematics 45, no. 4 (December 1, 1987): 691–94. http://dx.doi.org/10.1090/qam/917018.

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24

BENJAMINI, ITAI, and ODED SCHRAMM. "LACK OF SPHERE PACKING OF GRAPHS VIA NONLINEAR POTENTIAL THEORY." Journal of Topology and Analysis 05, no. 01 (March 2013): 1–11. http://dx.doi.org/10.1142/s1793525313500039.

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It is shown that there is no quasi-sphere packing of the lattice grid ℤd+1 or a co-compact hyperbolic lattice of [Formula: see text] or the 3-regular tree × ℤ, in ℝd, for all d. A similar result is proved for some other graphs too. Rather than using a direct geometrical approach, the main tools we are using are from nonlinear potential theory.

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25

Zhang, Junyong, and Jiqiang Zheng. "Scattering theory for nonlinear Schrödinger equations with inverse-square potential." Journal of Functional Analysis 267, no. 8 (October 2014): 2907–32. http://dx.doi.org/10.1016/j.jfa.2014.08.012.

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26

Ma, Chao, Yi Zhu, Jiayi He, Chenliang Zhang, Decheng Wan, Chi Yang, and Francis Noblesse. "Nonlinear corrections of linear potential-flow theory of ship waves." European Journal of Mechanics - B/Fluids 67 (January 2018): 1–14. http://dx.doi.org/10.1016/j.euromechflu.2017.07.006.

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27

Osano, Bob. "Dynamo Theory, Nonlinear Magnetic Fields, and the Euler Potentials." Advances in Astronomy 2018 (October 10, 2018): 1–6. http://dx.doi.org/10.1155/2018/4823494.

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The debate on the role of Euler potentials (EP), α∇β, in the dynamo theory is a long-standing one. It is known that the cross-product of gradients of two the potentials may represent magnetic fields lines. However, 2D and 3D dynamo hydromagnetic simulations suggest that their utility as analogues of magnetic field potential is restricted. This raises questions about their utility in the broader context of magneto-genesis and dynamo theories. We reexamine this and find that a reinterpretation of such potentials offers a new insight into the role EP may play in the general evolution of magnetic fields.

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28

El-Sayed, M. F., N. T. Eldabe, M. H. Haroun, and D. M. Mostafa. "Nonlinear electroviscoelastic potential flow instability theory of two superposed streaming dielectric fluids." Canadian Journal of Physics 92, no. 10 (October 2014): 1249–57. http://dx.doi.org/10.1139/cjp-2013-0446.

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The nonlinear electrohydrodynamic Kelvin–Helmholtz instability of two superposed viscoelastic Walters B′ dielectric fluids in the presence of a tangential electric field is investigated in three dimensions using the potential flow analysis. The method of multiple scales is used to obtain a dispersion relation for the linear problem, and a nonlinear Ginzburg–Landau equation with complex coefficients for the nonlinear problem. The linear and nonlinear stability conditions are obtained and discussed both analytically and numerically. In the linear stability analysis, we found that the fluid velocities and kinematic viscosities have destabilizing effects, and the electric field, kinematic viscoelasticities, and surface tension have stabilizing effects; and that the system in the three-dimensional disturbances is more stable than in the corresponding case of two-dimensional disturbances. While in the nonlinear analysis, for both two- and three-dimensional disturbances, we found that the fluid velocities, surface tension, and kinematic viscosities have destabilizing effects, and the electric field, kinematic viscoelasticities have stabilizing effects, and that the system in the three-dimensional disturbances is more unstable than its behavior in the two-dimensional disturbances for most physical parameters except the kinematic viscosities.

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29

Fishman, Shmuel, Yevgeny Krivolapov, and Avy Soffer. "Perturbation theory for the nonlinear Schrödinger equation with a random potential." Nonlinearity 22, no. 12 (October 30, 2009): 2861–87. http://dx.doi.org/10.1088/0951-7715/22/12/004.

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30

Gigli, Nicola, and Andrea Mondino. "A PDE approach to nonlinear potential theory in metric measure spaces." Journal de Mathématiques Pures et Appliquées 100, no. 4 (October 2013): 505–34. http://dx.doi.org/10.1016/j.matpur.2013.01.011.

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31

Luo, Dehai, Wenqi Zhang, Linhao Zhong, and Aiguo Dai. "A Nonlinear Theory of Atmospheric Blocking: A Potential Vorticity Gradient View." Journal of the Atmospheric Sciences 76, no. 8 (July 17, 2019): 2399–427. http://dx.doi.org/10.1175/jas-d-18-0324.1.

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Abstract In this paper, an extended nonlinear multiscale interaction model of blocking events in the equivalent barotropic atmosphere is used to investigate the effect of a slowly varying zonal wind in the meridional direction on dipole blocking that is regarded as a nonlinear Rossby wave packet. It is shown that the meridional gradient of potential vorticity (PVy=∂PV/∂y) prior to the blocking onset, which is related to the background zonal wind and its nonuniform meridional shear, can significantly affect the lifetime, intensity, and north–south asymmetry of dipole blocking, while the blocking dipole itself is driven by preexisting incident synoptic-scale eddies. The magnitude of the background PVy determines the energy dispersion and nonlinearity of blocking. It is revealed that a small background PVy is a prerequisite for strong and long-lived eddy-driven blocking that behaves as a persistent meandering westerly jet stream, while the blocking establishment further reduces the PVy within the blocking region, resulting in a positive feedback between blocking and PVy. When the core of the background westerly jet shifts from higher to lower latitudes, the blocking shows a northwest–southeast-oriented dipole with a strong anticyclonic anomaly to the northwest and a weak cyclonic anomaly to the southeast as its northern pole moves westward more rapidly and has weaker energy dispersion and stronger nonlinearity than its southern pole because of the smaller PVy in higher latitudes. The opposite is true when the background jet shifts toward higher latitudes. The asymmetry of dipole blocking vanishes when the background jet shows a symmetric double-peak structure. Thus, a small prior PVy is a favorable precursor for the occurrence of long-lived and large-amplitude blocking.

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32

Kinnunen, Juha. "Anders Björn and Jana Björn: “Nonlinear Potential Theory on Metric Spaces”." Jahresbericht der Deutschen Mathematiker-Vereinigung 115, no. 1 (February 6, 2013): 47–50. http://dx.doi.org/10.1365/s13291-013-0057-3.

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33

Kinnunen, Juha, Teemu Lukkari, and Mikko Parviainen. "Local approximation of superharmonic and superparabolic functions in nonlinear potential theory." Journal of Fixed Point Theory and Applications 13, no. 1 (March 2013): 291–307. http://dx.doi.org/10.1007/s11784-013-0108-5.

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34

Chapot, David, Lydéric Bocquet, and Emmanuel Trizac. "Electrostatic potential around charged finite rodlike macromolecules: nonlinear Poisson–Boltzmann theory." Journal of Colloid and Interface Science 285, no. 2 (May 2005): 609–18. http://dx.doi.org/10.1016/j.jcis.2004.11.059.

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35

FANG, WEI, H. Q. LU, and Z. G. HUANG. "COSMOLOGY IN NONLINEAR BORN–INFELD SCALAR FIELD THEORY WITH NEGATIVE POTENTIALS." International Journal of Modern Physics A 22, no. 12 (May 10, 2007): 2173–95. http://dx.doi.org/10.1142/s0217751x07036750.

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The cosmological evolution in Nonlinear Born–Infeld (hereafter NLBI) scalar field theory with negative potentials was investigated. The cosmological solutions in some important evolutive epoches were obtained. The different evolutional behaviors between NLBI and linear (canonical) scalar field theory have been presented. A notable characteristic is that NLBI scalar field behaves as ordinary matter nearly the singularity while the linear scalar field behaves as "stiff" matter. We find that in order to accommodate current observational accelerating expanding universe the value of potential parameters |m| and |V0| must have an upper bound. We compare different cosmological evolutions for different potential parameters m, V0.

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36

Papageorgiou, Nikolaos S., Vicenţiu D. Rădulescu, and Dušan D. Repovš. "Nonlinear singular problems with indefinite potential term." Analysis and Mathematical Physics 9, no. 4 (June 24, 2019): 2237–62. http://dx.doi.org/10.1007/s13324-019-00333-7.

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37

Hasanov, Alemdar. "Monotonicity of nonlinear boundary value problems related to deformation theory of plasticity." Mathematical Problems in Engineering 2006 (2006): 1–18. http://dx.doi.org/10.1155/mpe/2006/58143.

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We study nonlinear boundary value problems arising in the deformation theory of plasticity. These problems include 3D mixed problems related to nonlinear Lame system, elastoplastic bending of an incompressible hardening plate, and elastoplastic torsion of a bar. For all these different problems, we present a general variational approach based on monotone potential operator theory and prove solvability and monotonicity of potentials. The obtained results are illustrated on numerical examples.

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38

RODRIGUES, R. DE LIMA. "NEW POTENTIAL SCALAR MODELS VIA THE KINK OF THE λΦ4 THEORY." Modern Physics Letters A 10, no. 18 (June 14, 1995): 1309–16. http://dx.doi.org/10.1142/s0217732395001435.

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From a scalar field theory in 1+1 dimensions, new nonlinear potential models have been found leading to an enlargement of potential classes that can be solved exactly in the context of quantum and classical theories. The method consists in considering a SUSY N=2 general solution for an unnormalizable state of the supersymmetric partner associated with the zero mode, which provides us with a new class of isospectral potentials that can be expressed in terms of the kink. The model considered here is a double-well potential, the kink of the λΦ4 theory. This self-interaction is part of the interaction that appears in the new potentials.

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39

NOVELLO, M., and S. L. S. DUQUE. "NONLOCAL THEORY OF GRAVITY." International Journal of Modern Physics D 04, no. 01 (February 1995): 79–96. http://dx.doi.org/10.1142/s0218271895000065.

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We use a three-index tensor Aμνα to describe spin-2 fields. This quantity acts as the potential of the standard variable hμν. We apply the new variables to examine the coherence of a nonlocal nonlinear theory of gravity.

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40

Shen, Yao Tian, and Yang Xin Yao. "Nonlinear elliptic equations with critical potential and critical parameter." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 136, no. 5 (October 2006): 1041–51. http://dx.doi.org/10.1017/s030821050000487x.

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We give a positive answer to an open problem about Hardy's inequality raised by Brézis and Vázquez, and another result obtained improves that of Vázquez and Zuazua. Furthermore, by this improved inequality and the critical-point theory, in a k-order Sobolev–Hardy space, we obtain the existence of multi-solution to a nonlinear elliptic equation with critical potential and critical parameter.

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41

Gibara, Ryan, and Richard L. Hall. "Potential envelope theory and the local energy theorem." Journal of Mathematical Physics 60, no. 6 (June 2019): 062103. http://dx.doi.org/10.1063/1.5064456.

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42

Quick, R. M., and S. G. Sharapov. "The Coleman-Weinberg effective potential in superconductivity theory." Theoretical and Mathematical Physics 122, no. 3 (March 2000): 390–401. http://dx.doi.org/10.1007/bf02551252.

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43

O'DWYER, JAMES P. "NONPERTURBATIVE TACHYON POTENTIAL FROM THE WILSONIAN RENORMALIZATION GROUP." Modern Physics Letters A 20, no. 11 (April 10, 2005): 807–11. http://dx.doi.org/10.1142/s0217732305017135.

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The derivative expansion of the Wilsonian renormalization group generates additional terms in the effective β-functions not present in the perturbative approach. Applied to the nonlinear σ-model, to lowest order the vanishing of the β-function for the tachyon field generates an equation analogous to that found in open string field theory. Although the nonlinear term depends on the cutoff function, this arbitrariness can be removed by a rescaling of the tachyon field.

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44

Verbitsky, Igor. "Quasilinear elliptic equations with sub-natural growth terms and nonlinear potential theory." Rendiconti Lincei - Matematica e Applicazioni 30, no. 4 (November 5, 2019): 733–58. http://dx.doi.org/10.4171/rlm/869.

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45

Filippakis, Michael E., and Nikolaos S. Papageorgiou. "Solutions for nonlinear variational inequalities with a nonsmooth potential." Abstract and Applied Analysis 2004, no. 8 (2004): 635–49. http://dx.doi.org/10.1155/s1085337504312017.

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First we examine a resonant variational inequality driven by thep-Laplacian and with a nonsmooth potential. We prove the existence of a nontrivial solution. Then we use this existence theorem to obtain nontrivial positive solutions for a class of resonant elliptic equations involving thep-Laplacian and a nonsmooth potential. Our approach is variational based on the nonsmooth critical point theory for functionals of the formφ=φ1+φ2withφ1locally Lipschitz andφ2proper, convex, lower semicontinuous.

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46

KUZNETSOVA, A. YU, A. P. KUZNETSOV, C. KNUDSEN, and E. MOSEKILDE. "CATASTROPHE THEORETIC CLASSIFICATION OF NONLINEAR OSCILLATORS." International Journal of Bifurcation and Chaos 14, no. 04 (April 2004): 1241–66. http://dx.doi.org/10.1142/s0218127404009995.

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Catastrophe theory is employed to classify different types of nonlinear oscillators, basing on the complication of their potentials. By using Thom's catastrophe unfoldings as oscillator potentials, we have introduced more general models to describe the dynamics of nonlinear oscillators, differing from each other by the form of their potential wells and by the possibility of escape. Spreading the investigation in the space of the parameters of the potential function, we have revealed that our examples defined via Thom's catastrophe unfoldings have some type of universal properties in the context of forced oscillations. For oscillators with nonescaping solutions, we have detected such typical bifurcation structures as crossroad areas and spring areas, and have described the universal scenario of their evolution under the forcing amplitude variation. On increasing the potential function degree, the complexity of the charts of the dynamical regimes results from the repetition of the described bifurcation scenario. For oscillators with escaping solutions, such general properties were investigated, as dependence of the charts of the dynamical regimes and the basins on the parameters of the potential function. We have observed that these properties are typical in a broad range of the control parameters.

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47

Hussein, Mahir S., Weibin Li, and Sebastian Wüster. "Canonical quantum potential scattering theory." Journal of Physics A: Mathematical and Theoretical 41, no. 47 (October 20, 2008): 475207. http://dx.doi.org/10.1088/1751-8113/41/47/475207.

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48

GELLER, MICHAEL R. "DENSITY FUNCTIONAL THEORY AND STATISTICAL GAUGE FIELDS." Modern Physics Letters B 07, no. 29n30 (December 30, 1993): 1941–46. http://dx.doi.org/10.1142/s021798499300196x.

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We consider the possibility that the exchange-correlation vector potential of density functional theory and the Chern-Simons gauge potential, used to change the statistics of particles in two dimensions, are related. By comparing the corresponding gauge invariant field strengths and their dependence on density and external magnetic field, we find no connection between these two potentials, in contrast to a recent proposal.

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49

Saanouni, Tarek. "Potential well theory for the focusing fractional Choquard equation." Journal of Mathematical Physics 61, no. 6 (June 1, 2020): 061502. http://dx.doi.org/10.1063/5.0002234.

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50

Vyblyi, Yu P. "Nonsymmetrical tensor potential in the relativistic theory of gravity." Theoretical and Mathematical Physics 123, no. 3 (June 2000): 851–57. http://dx.doi.org/10.1007/bf02551039.

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