On uniqueness of entropy solutions for nonlinear elliptic degenerate anisotropic equations

Author
Yu. S. Gorban
Donetsk National University, Vinnytsia, Ukraine
Abstract
In the present paper we deal with the Dirichlet problem for a class of degenerate anisotropic elliptic second-order equations with $L^1$-right-hand sides in a bounded domain of ${\Bbb R}^n$ $(n \geqslant 2)$. This class is described by the presence of a set of exponents $q_1,\dots,q_n$ and a set of weighted functions $\nu_1,\dots,\nu_n$ in growth and coercitivity conditions on coefficients of the equations. The exponents $q_i$ characterize the rates of growth of the coefficients with respect to the corresponding derivatives of unknown function, and the functions $\nu_i$ characterize degeneration or singularity of the coefficients with respect to independent variables. Our aim is to study the uniqueness of entropy solution of the problem under consideration.
Keywords
nonlinear elliptic degenerate anisotropic second-order equations; $L^1$-data; Dirichlet problem; uniqueness of entropy solution
DOI
doi:10.15330/ms.47.1.59-70
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Pages
59-70
Volume
47
Issue
1
Year
2017
Journal
Matematychni Studii
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