Calculus of Variations and Geometric Measure Theory

P. Bousquet - L. Brasco - C. Leone - A. Verde

On the Lipschitz character of orthotropic $p-$harmonic functions

created by brasco on 21 Apr 2017
modified on 12 Apr 2018


Accepted Paper

Inserted: 21 apr 2017
Last Updated: 12 apr 2018

Journal: Calc. Var. Partial Differential Equations
Pages: 34
Year: 2017


We prove that local weak solutions of the orthotropic $p-$harmonic equation are locally Lipschitz, for every $p\ge 2$ and in every dimension. More generally, the result holds true for more degenerate equations with orthotropic structure, with right-hand sides in suitable Sobolev spaces.

Keywords: Degenerate elliptic equations, Lipschitz regularity, Anisotropic problems, orthotropic problems