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

Saara Sarsa | Zendy

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Note 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.

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