Calculus of Variations and Geometric Measure Theory

L. Brasco - F. Santambrogio

A sharp estimate à la Calderón-Zygmund for the $p-$Laplacian

created by santambro on 20 Jul 2016
modified by brasco on 09 Mar 2017


Accepted Paper

Inserted: 20 jul 2016
Last Updated: 9 mar 2017

Journal: Commun. Contemp. Math.
Pages: 22 pages
Year: 2017
Doi: 10.1142/S0219199717500304


We consider local weak solutions of the Poisson equation for the $p-$Laplace operator. We prove a higher differentiability result, under an essentially sharp condition on the right-hand side. The result comes with a local scaling invariant a priori estimate.

Keywords: fractional Sobolev spaces, regularity of solutions, Degenerate quasilinear elliptic equations, higher differentiability