SOLVABILITY OF DEGENERATE ANISOTROPIC ELLIPTIC SECOND-ORDER EQUATIONS WITH L1-DATA

被引：0

作者：

Kovalevsky, Alexander A. ^{[1
]}

Gorban, Yuliya S. ^{[2
]}

机构：

[1] Natl Acad Sci Ukraine, Inst Appl Math & Mech, Dept Nonlinear Anal, Donetsk, Ukraine

[2] Donetsk Natl Univ, Dept Differential Equat, Donetsk, Ukraine

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2013年

关键词：

Degenerate anisotropic elliptic second-order equations; L-1-data; Dirichlet problem; entropy solution; T-solution; W-solution; weighted weak solution; existence of solutions; ENTROPY SOLUTIONS; DIRICHLET PROBLEM; VARIATIONAL-INEQUALITIES; PARABOLIC EQUATIONS; EXISTENCE;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we study the Dirichlet problem for degenerate anisotropic elliptic second-order equations with L-1-right-hand sides on a bounded open set of R-n (n >= 2). These equations are described with a set of exponents and of a set of weighted functions. The exponents characterize the rates of growth of the coefficients of the equations with respect to the corresponding derivatives of the unknown function, and the weighted functions characterize degeneration or singularity of the coefficients of the equations with respect to the spatial variable. We prove theorems on the existence of entropy solutions, T-solutions, W-solutions, and weighted weak solutions of the problem under consideration.

引用

页数：17

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