Inserted: 2 jun 2012
Last Updated: 20 mar 2014
Journal: J. Convex Anal.
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