Note on an elementary inequality and its application to the regularity of p-harmonic functions

Authors

  • Saara Sarsa University of Helsinki, Department of Mathematics and Statistics

DOI:

https://doi.org/10.54330/afm.112699

Keywords:

p-harmonic function, Sobolev regularity, elementary inequality

Abstract

We study the Sobolev regularity of \(p\)-harmonic functions. We show that \(|Du|^{\frac{p-2+s}{2}}Du\) belongs to the Sobolev space \(W^{1,2}_{\operatorname{loc}}\), \(s>-1-\frac{p-1}{n-1}\), for any \(p\)-harmonic function \(u\). The proof is based on an elementary inequality.

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Published

2021-12-09

Issue

Vol. 47 No. 1 (2022)

Section

Articles

License

Copyright (c) 2021 Annales Fennici Mathematici

Creative Commons License

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

How to Cite

Sarsa, S. (2021). Note on an elementary inequality and its application to the regularity of p-harmonic functions. Annales Fennici Mathematici, 47(1), 139-153. https://doi.org/10.54330/afm.112699