Continuous imbedding in Musielak spaces with an application to anisotropic nonlinear Neumann problems

Abstract

We prove a continuous embedding that allows us to obtain a boundary trace imbedding result for anisotropic Musielak-Orlicz spaces, which we then apply to obtain an existence result for Neumann problems with nonlinearities on the boundary associated to some anisotropic nonlinear elliptic equations in Musielak-Orlicz spaces constructed from Musielak-Orlicz functions on which and on their conjugates we do not assume the \(\Delta_2\)-condition. The uniqueness of weak solutions is also studied.
 For more information see https://ejde.math.txstate.edu/Volumes/2021/26/abstr.html