Pointwise inequalities for Sobolev functions on generalized cuspidal domains

Authors

  • Zheng Zhu University of Jyväskylä, Department of Mathematics and Statistics

DOI:

https://doi.org/10.54330/afm.117881

Keywords:

Sobolev functions, cuspidal domains, pointwise inequality

Abstract

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 \(W^{1, p}(\Omega)=M^{1, p}(\Omega)\).

 

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Published

2022-05-10

Issue

Vol. 47 No. 2 (2022)

Section

Articles

License

Copyright (c) 2022 Annales Fennici Mathematici

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

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