Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 20 (2013), No. 4, 901--918Copyright Heldermann Verlag 2013 Fractional Regularity for Nonlinear Elliptic Problems with Measure Data Agnese Di Castro Dip. di Matematica, Università degli Studi di Parma, Campus - Parco Area delle Scienze 53/A, 43124 Parma, Italy agnese.dicastro@unipr.it Giampiero Palatucci Dip. di Matematica, Università 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 [ Fulltext-pdf  (182  KB)] for subscribers only.