Musielak-Orlicz-Sobolev embeddings: Necessary and Sufficient Conditions

Abstract

In this paper we study the necessary and sufficient conditions on domain for Musielak-Orlicz-Sobolev embedding of the space $W^{1,\Phi (\cdot ,\cdot )}(\Omega )$ where $\Phi (x,t):=t^{p(x)}{(\log (e+t))}^{q(x)}.$

16 pages