Open AccessNote on an elementary inequality and its application to the regularity of p-harmonic functions
Author(s) -
Saara Sarsa
Publication year - 2021
Publication title -
annales fennici mathematici
Language(s) - English
Resource type - Journals
eISSN - 2737-114X
pISSN - 2737-0690
DOI - 10.54330/afm.112699
Subject(s) - elementary proof , harmonic function , mathematics , sobolev space , harmonic , elementary function , pure mathematics , inequality , function (biology) , space (punctuation) , sobolev inequality , combinatorics , mathematical analysis , physics , quantum mechanics , computer science , evolutionary biology , biology , operating system
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.