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Relevant bibliographies by topics / Degenerate elliptic equation

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Journal articles

Academic literature on the topic 'Degenerate elliptic equation'

Author: Grafiati

Published: 11 March 2023

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Journal articles on the topic "Degenerate elliptic equation"

1

Trudinger, Neil S. "On degenerate fully nonlinear elliptic equations in balls." Bulletin of the Australian Mathematical Society 35, no. 2 (1987): 299–307. http://dx.doi.org/10.1017/s0004972700013253.

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We establish derivative estimates and existence theorems for the Dirichlet and Neumann problems for nonlinear, degenerate elliptic equations of the form F (D2u) = g in balls. The degeneracy arises through the possible vanishing of the function g and the degenerate Monge-Ampère equation is covered as a special case.

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2

Igisinov, S. Zh, L. D. Zhumaliyeva, A. O. Suleimbekova, and Ye N. Bayandiyev. "Estimates of singular numbers (s-numbers) for a class of degenerate elliptic operators." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 107, no. 3 (2022): 51–58. http://dx.doi.org/10.31489/2022m3/51-58.

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In this paper we study a class of degenerate elliptic equations with an arbitrary power degeneracy on the line. Based on the research carried out in the course of the work, the authors propose methods to overcome various difficulties associated with the behavior of functions from the definition domain for a differential operator with piecewise continuous coefficients in a bounded domain, which affect the spectral characteristics of boundary value problems for degenerate elliptic equations. It is shown the conditions imposed on the coefficients at the lowest terms of the equation, which ensure

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3

Le, Nam Q. "On the Harnack inequality for degenerate and singular elliptic equations with unbounded lower order terms via sliding paraboloids." Communications in Contemporary Mathematics 20, no. 01 (2017): 1750012. http://dx.doi.org/10.1142/s0219199717500122.

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We use the method of sliding paraboloids to establish a Harnack inequality for linear, degenerate and singular elliptic equation with unbounded lower order terms. The equations we consider include uniformly elliptic equations and linearized Monge–Ampère equations. Our argument allows us to prove the doubling estimate for functions which, at points of large gradient, are solutions of (degenerate and singular) elliptic equations with unbounded drift.

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4

Tanirbergen, Aisulu K. "A MIXED PROBLEM FOR A DEGENERATE MULTIDIMENSIONAL ELLIPTIC EQUATION." UNIVERSITY NEWS. NORTH-CAUCASIAN REGION. NATURAL SCIENCES SERIES, no. 3 (211) (September 30, 2021): 37–41. http://dx.doi.org/10.18522/1026-2237-2021-3-37-41.

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This article shows the unique solvability and obtains an explicit form of the classical solution of the mixed prob-lem in a cylindrical domain for a model degenerate multidimensional elliptic equation. The correctness of boundary value problems in the plane for elliptic equations by the method of the theory of ana-lytic functions of a complex variable has been well studied. The first boundary value problem or the Dirichlet problem for multidimensional elliptic equations with degeneration on the boundary has been sufficiently analyzed. However, as we know, the mixed problem for the indicated eq

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5

Andreu, F., V. Caselles, and J. M. Mazón. "A strongly degenerate quasilinear elliptic equation." Nonlinear Analysis: Theory, Methods & Applications 61, no. 4 (2005): 637–69. http://dx.doi.org/10.1016/j.na.2004.11.020.

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6

Krasovitskii, T. I. "Degenerate elliptic equations and nonuniqueness of solutions to the Kolmogorov equation." Доклады Академии наук 487, no. 4 (2019): 361–64. http://dx.doi.org/10.31857/s0869-56524874361-364.

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In this paper we propose a new method of constructing examples of nonuniqueness of probability solutions by reducing the stationary Fokker-Planck-Kolmogorov equation to a degenerate elliptic equation on a bounded domain.

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7

Rocca, Elisabetta, and Riccarda Rossi. "A degenerating PDE system for phase transitions and damage." Mathematical Models and Methods in Applied Sciences 24, no. 07 (2014): 1265–341. http://dx.doi.org/10.1142/s021820251450002x.

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In this paper, we analyze a PDE system arising in the modeling of phase transition and damage phenomena in thermoviscoelastic materials. The resulting evolution equations in the unknowns ϑ (absolute temperature), u (displacement), and χ (phase/damage parameter) are strongly nonlinearly coupled. Moreover, the momentum equation for u contains χ-dependent elliptic operators, which degenerate at the pure phases (corresponding to the values χ = 0 and χ = 1), making the whole system degenerate. That is why, we have to resort to a suitable weak solvability notion for the analysis of the problem: it c

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8

Gutiérrez, Cristian E., and Federico Tournier. "Harnack Inequality for a Degenerate Elliptic Equation." Communications in Partial Differential Equations 36, no. 12 (2011): 2103–16. http://dx.doi.org/10.1080/03605302.2011.618210.

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9

Horiuchi, Toshio. "Quasilinear degenerate elliptic equation with absorption term." Nonlinear Analysis: Theory, Methods & Applications 47, no. 3 (2001): 1649–57. http://dx.doi.org/10.1016/s0362-546x(01)00298-x.

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10

Amano, Kazuo. "The Dirichlet problem for degenerate elliptic 2-dimensional Monge-Ampère equation." Bulletin of the Australian Mathematical Society 37, no. 3 (1988): 389–410. http://dx.doi.org/10.1017/s0004972700027015.

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We study the following Dirichlet problem for the degenerate elliptic Monge-Ampère equation: Given , f ≥ 0 and , find a solution , t ≥ 2, satisfying in Ω and u = g on ∂Ω. Since f is nonnegative, we cannot apply any standard elliptic methods. In this paper, we use an iteration scheme of Nash-Moser type and a priori estimates for degenerate elliptic operators, and solve the Dirichlet problem for a certain class of f and g.

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