On a compact trace embedding theorem in Musielak-Sobolev spaces

TL;DR

This paper establishes a stronger compact boundary embedding theorem in Musielak-Orlicz-Sobolev spaces and applies it to solve nonlinear elliptic equations with Neumann boundary conditions using variational methods.

Contribution

It introduces a new compact embedding theorem in Musielak-Orlicz-Sobolev spaces and demonstrates its application to nonlinear elliptic boundary value problems.

Findings

Proved a stronger boundary embedding theorem.

Applied the theorem to nonlinear elliptic equations.

Achieved existence results for solutions with Neumann boundary conditions.

Abstract

By a stronger compact boundary embedding theorem in Musielak-Orlicz-Sobolev space developed in the paper, variational method is employed to deal with the nonlinear elliptic equation with the nonlinear Neumann boundary condition in the framework of Musielak-Orlicz-Sobolev space.