Degenerate Elliptic Equations with Nonlinear Boundary Conditions and Measures Data

Abstract

In this paper we study the questions of existence and uniqueness of solutions for equations of type −div a(x, Du) + γ( u) � µ1, posed in an open bounded subsetof R N , with nonlinear boundary conditions of the form a(x, Du)·η+β(u) � µ2. The nonlinear elliptic operator div a(x, Du) is modeled on the p-Laplacian operatorp(u) = div (|Du| p−2 Du), with p > 1, γ and β are maximal monotone graphs in R 2 such that 0 ∈ γ( 0) ∩ β(0) and the data µ1 and µ2 are measures.