Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 167, pp. 117.
Solvability of degenerate anisotropic elliptic
secondorder equations with
data
Alexander A. Kovalevsky, Yuliya S. Gorban
Abstract:
In this article, we study the Dirichlet problem for degenerate anisotropic
elliptic secondorder equations with
righthand 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, Tsolutions,
Wsolutions, 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 secondorder equations;
L1data; Dirichlet problem; entropy solution; Tsolution;
Wsolution; 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
email: alexkvl@iamm.ac.donetsk.ua


Yuliya S. Gorban
Department of Differential Equations
Donetsk National University, Donetsk, Ukraine
email: yuliya_gorban@mail.ru

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