Musielak-Orlicz-Sobolev embeddings: Necessary and Sufficient Conditions (2406.08091v2)

Published 12 Jun 2024 in math.FA

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 $\Phi(x,t):=t^{{p(x)}{(\log(e+t))}^{q(x)}.$}