Espaces d'Orlicz, Orlicz-Sobolev et application aux E-D-P

TL;DR

This paper introduces Orlicz and Orlicz-Sobolev spaces, explores their topological properties, and applies them to solving partial differential equations using variational methods.

Contribution

It develops the theory of Orlicz and Orlicz-Sobolev spaces and demonstrates their application to PDEs, expanding the functional analytic tools available for such problems.

Findings

Established the topological properties of Orlicz and Orlicz-Sobolev spaces.

Applied these spaces to variational methods for PDEs.

Provided new insights into solving PDEs with non-standard growth conditions.

Abstract

In this article, we will define the Orlicz space and the Orlicz-Sobolev space, and develop their topological properties. We will also examine their applications to partial differential equations (PDEs), with an emphasis on the use of certain variational methods.