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Musielak-Orlicz-Sobolev embeddings: Necessary and Sufficient Conditions

Functional Analysis 2025-05-21 v2
Authors: Ankur Pandey , Nijjwal Karak
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Abstract

In this paper we study the necessary and sufficient conditions on domain for Musielak-Orlicz-Sobolev embedding of the space W1,Φ(⋅,⋅)(Ω)W^{1,\Phi(\cdot,\cdot)}(\Omega) where Φ(x,t):=tp(x)(log⁡(e+t))q(x).\Phi(x,t):=t^{p(x)}{(\log(e+t))}^{q(x)}.

Keywords

Musielak-Orlicz Sobolev embedding necessary and sufficient conditions domain conditions

Cite

@article{arxiv.2406.08091,
  title  = {Musielak-Orlicz-Sobolev embeddings: Necessary and Sufficient Conditions},
  author = {Ankur Pandey and Nijjwal Karak},
  journal= {arXiv preprint arXiv:2406.08091},
  year   = {2025}
}

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16 pages

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