Analysis & PDE Vol. 11, No. 4, 2018

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$C^1$ regularity of orthotropic $p$-harmonic functions in the plane

Pierre Bousquet and Lorenzo Brasco

Vol. 11 (2018), No. 4, 813–854

DOI: 10.2140/apde.2018.11.813

Abstract

We prove that local weak solutions of the orthotropic $p$ -harmonic equation in $ℝ^{2}$ are $C^{1}$ functions.

Keywords

degenerate and singular problems, regularity of minimizers

Mathematical Subject Classification 2010

Primary: 49N60, 49K20, 35B65

Milestones

Received: 31 August 2016

Revised: 30 August 2017

Accepted: 24 October 2017

Published: 12 January 2018

Authors

Pierre Bousquet
Institut de Mathématiques de Toulouse, CNRS UMR 5219 Université de Toulouse Toulouse France

Lorenzo Brasco
Dipartimento di Matematica e Informatica Università degli Studi di Ferrara Ferrara Italy	Institut de Mathématiques de Marseille Aix-Marseille Université Marseille France