Geodesic
Fractional Regularity for Nonlinear Elliptic Problems with Measure Data
Journal of convex analysis, Tome 20 (2013) no. 4, pp. 901-918

Voir la notice de l'article provenant de la source Heldermann Verlag

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].
Classification : 35J60, 35J70
Mots-clés : Nonlinear elliptic problems, Calderon-Zygmund theory, Measure data, Fractional differentiability, Fractional Sobolev spaces 
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     title = {Fractional {Regularity} for {Nonlinear} {Elliptic} {Problems} with {Measure} {Data}},
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     pages = {901--918},
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A. Di Castro; G. Palatucci. Fractional Regularity for Nonlinear Elliptic Problems with Measure Data. Journal of convex analysis, Tome 20 (2013) no. 4, pp. 901-918. http://geodesic.mathdoc.fr/item/JCA_2013_20_4_JCA_2013_20_4_a0/