Abstract

We consider nonlinear elliptic equations of the type −div a(x,Du)=μ-\text{\rm div}\,a(x, Du)=\mu having a Radon measure on the right-hand side and prove fractional differentiability results of Calderón-Zygmund type for very weak solutions. We extend some of the results achieved by G. Mingione [``The Calderón-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].

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Nonlinear elliptic problems
  • Calderón-Zygmund theory
  • Measure data
  • Fractional differentiability
  • Fractional Sobolev spaces

Mathematics Subject Classification

35J60; 35J70

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Suggested citation

A. Di Castro, G. Palatucci. “Fractional Regularity for Nonlinear Elliptic Problems with Measure Data.” Journal of Convex Analysis 20 (2013), No. 4, 901–918. https://doi.org/10.68381/jca20048

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Published by Heldermann Verlag, 2013. Rights now held by Banach Press.