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Journal of Convex Analysis 20 (2013), No. 4, 901--918
Copyright Heldermann Verlag 2013



Fractional Regularity for Nonlinear Elliptic Problems with Measure Data

Agnese Di Castro
Dip. di Matematica, UniversitÓ degli Studi di Parma, Campus - Parco Area delle Scienze 53/A, 43124 Parma, Italy
agnese.dicastro@unipr.it

Giampiero Palatucci
Dip. di Matematica, UniversitÓ degli Studi di Parma, Campus - Parco Area delle Scienze 53/A, 43124 Parma, Italy
giampiero.palatucci@unimes.fr



[Abstract-pdf]

We consider nonlinear elliptic equations of the type $$ -\text{\rm div}\,a(x, Du)=\mu $$ having a Radon measure on the right-hand side and prove fractional differentiability results of Calder\'on-Zygmund type for very weak solutions. We extend some of the results achieved by G. Mingione [``The Calder\'on-Zygmund theory for elliptic problems with measure data'', Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 6 (2007) 195--261], in turn improving a regularity result by G. R. Cirmi and S. Leonardi [``Higher differentiability for solutions of linear elliptic systems with measure data'', Discrete Contin. Dyn. Syst. 26 (2010) 89--104].

Keywords: Nonlinear elliptic problems, Calderon-Zygmund theory, Measure data, Fractional differentiability, Fractional Sobolev spaces.

MSC: 35J60; 35J70

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