Multivalued anisotropic problem with Fourier boundary condition involving diffuse Radon measure data and variable exponents

Abstract

We study a nonlinear anisotropic elliptic problem under Fourier type boundary condition governed by a general anisotropic operator with variable exponents and diffuse Radon measure data which does not charge the sets of zero p(•)-capacity. We prove an existence and uniqueness result of entropy or renormalized solution.