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

2020/09/21 by Saara Sarsa, Sarsa, Saara
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.2009.10102

15 pages

arxiv created 2020/09/21 · arxiv updated 2020/09/23

Abstract

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

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