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We consider non-linear elliptic equations having a measure in the right-hand side, of the type 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.
@article{ASNSP_2007_5_6_2_195_0,
author = {Mingione, Giuseppe},
title = {The {Calder\'on-Zygmund} theory for elliptic problems with measure data},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {195--261},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 6},
number = {2},
year = {2007},
mrnumber = {2352517},
zbl = {1178.35168},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_2_195_0/}
}
TY - JOUR AU - Mingione, Giuseppe TI - The Calderón-Zygmund theory for elliptic problems with measure data JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2007 SP - 195 EP - 261 VL - 6 IS - 2 PB - Scuola Normale Superiore, Pisa UR - http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_2_195_0/ LA - en ID - ASNSP_2007_5_6_2_195_0 ER -
%0 Journal Article %A Mingione, Giuseppe %T The Calderón-Zygmund theory for elliptic problems with measure data %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2007 %P 195-261 %V 6 %N 2 %I Scuola Normale Superiore, Pisa %U http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_2_195_0/ %G en %F ASNSP_2007_5_6_2_195_0
Mingione, Giuseppe. The Calderón-Zygmund theory for elliptic problems with measure data. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 6 (2007) no. 2, pp. 195-261. http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_2_195_0/