Calculus of Variations and Geometric Measure Theory
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G. Mingione

The Calderón-Zygmund theory for elliptic problems with measure data

created by mingione on 29 Sep 2012


Published Paper

Inserted: 29 sep 2012
Last Updated: 29 sep 2012

Journal: Ann. Scu. Norm. Sup. Cl. Sci. (5)
Volume: 6
Pages: 195-261
Year: 2007


We consider non-linear elliptic equations having a measure in the right hand side, of the type $ \mbox{div}\ a(x,Du)=\mu, $ and prove differentiability and integrability results for solutions. New estimates in Marcinkiewicz spaces are also given, and the impact of the measure datum density properties on the regularity of solutions is analyzed in order to build a suitable Calderón-Zygmund theory for the problem. All the regularity results presented in this paper are provided together with explicit local a priori estimates

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