ON UNIQUENESS OF ENTROPY SOLUTIONS FOR NONLINEAR ELLIPTIC DEGENERATE ANISOTROPIC EQUATIONS

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 R^n (n > 2). This class is described by the presence of a set of exponents q1, . . . , qn and a set of weighted functions ν1, . . . , νn in growth and coercitivity conditions on coefficients of the equations. The exponents qi characterize the rates of growth of the coefficients with respect to the corresponding derivatives of unknown function, and the functions νi 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.