Calculus of Variations and Geometric Measure Theory

A. Di Castro - G. Palatucci

Fractional regularity for nonlinear elliptic problems with measure data

created by palatucci on 02 Jun 2012
modified on 20 Mar 2014


Published Paper

Inserted: 2 jun 2012
Last Updated: 20 mar 2014

Journal: J. Convex Anal.
Volume: 20
Number: 4
Pages: 901-918
Year: 2013


We consider nonlinear elliptic equations of the type $-div \, a(x, Du) = \mu$ having a Radon measure on the right-hand side and prove fractional differentiability results of Calderòn-Zygmund type for very weak solutions. We extend some of the results achieved by G. Mingione (Ann. Scu. Norm. Sup., 2007), in turn improving a regularity result by Cirmi & Leonardi (DCDS-A, 2010).

Keywords: measure data, fractional Sobolev spaces, Nonlinear elliptic problems, Calderon-Zygmund theory, Fractional differentiability