Some properties of Musielak spaces with only the log-Hölder continuity condition and application

Abstract

In this paper, we prove a density and a duality results in Musielak spaces, as well as an inequality of type Poincare, assuming only the log-Holder continuity condition. We will apply these results to give in non reflexive Musielak spaces the existence of solutions for some nonlinear parabolic problems with no continuous lower order terms.