Existence of entropy solutions for nonlinear elliptic degenerate anisotropic equations

Abstract

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.