Existence and uniqueness of entropy solution for nonlinear elliptic equation with nonlinear boundary conditions and measure-data

Abstract

The aim of this paper is to study, for measure-data, the existence and uniqueness of solutions for nonlinear equation type: b(u) - div a(u, Du) = ν, subject to nonlinear boundary conditions of the form -a(u, Du).η ∈ β(x, u). To establish both the existence and uniqueness of
the solution, the concept of entropy solution is employed in this study.

Keywords: Non-linear problem ; Entropy solution ; Nonlinear boundary conditions ; Measure-data.
2020 Mathematics Subject Classifications. Primary 35J60, 35J66; Secondary 35R06.