Alexander A. Kovalevsky, Yuliya S. Gorban
In this article, we study the Dirichlet problem for degenerate anisotropic elliptic second-order equations with -right-hand sides on a bounded open set of ( ). 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.
Submitted November 28, 2012. Published July 22, 2013.
Math Subject Classifications: 35J25, 35J60, 35J70, 35R05.
Key Words: Degenerate anisotropic elliptic second-order equations; L1-data; Dirichlet problem; entropy solution; T-solution; W-solution; weighted weak solution; existence of solutions.
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| Alexander A. Kovalevsky |
Department of Nonlinear Analysis
Institute of Applied Mathematics and Mechanics
National Academy of Sciences of Ukraine, Donetsk, Ukraine
| Yuliya S. Gorban |
Department of Differential Equations
Donetsk National University, Donetsk, Ukraine
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