Existence of entropy solutions for nonlinear elliptic degenerate anisotropic equations
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2017
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Анотація
In the present article 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 R^n (n >=2). This class is described by
the presence of a set of exponents q_1,...., q_n and a set of weighted functions v_1,....., v_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 v_i characterize degeneration or
singularity of the coefficients with respect to independent variables. Our aim is to investigate the existence of entropy
solutions of the problem under consideration.
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Ключові слова
Nonlinear elliptic degenerate anisotropic second-order equations, L1 -data, Dirichlet problem, Existence of entropy solutions