Pointwise inequalities for Sobolev functions on generalized cuspidal domains
Keywords:
Sobolev functions, cuspidal domains, pointwise inequalityAbstract
Let \(\Omega\subset\mathbb{R}^{n-1}\) be a bounded star-shaped domain and \(\Omega_\psi\) be an outward cuspidal domain with base domain \(\Omega\). We prove that for \(1<p\leq\infty\), \(W^{1, p}(\Omega_\psi)=M^{1,p}(\Omega_\psi)\) if and only if \(W^{1, p}(\Omega)=M^{1, p}(\Omega)\).
How to Cite
Zhu, Z. (2022). Pointwise inequalities for Sobolev functions on generalized cuspidal domains. Annales Fennici Mathematici, 47(2), 747–757. https://doi.org/10.54330/afm.117881
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