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Publication Date:
February 2010
ISSN:
1435-5337
DOI:
10.1515/forum.2010.048

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Forum Mathematicum

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Regularity results for the gradient of solutions of linear elliptic systems with VMO-coefficients and L1,λ data

Salvatore Leonardi1 / Jana Stará2

1Dipartimento di Matematica ed Informatica, Università di Catania, Viale A. Doria 6, 95125 Catania, Italy. leonardi@dmi.unict.it

2Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic. stara@karlin.mff.cuni.cz

Citation Information: Forum Mathematicum. Volume 22, Issue 5, Pages 913–940, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: 10.1515/forum.2010.048, February 2010

Publication History:
Received:
2007-10-02
Revised:
2008-07-07
Published Online:
2010-02-12

Abstract

We prove that if a vector-function ƒ belongs to the Morrey space , with , n ≥ 3, N ≥ 2, λ ∈ [0, n – 2], then there exists a very weak solution u of the system

such that Du belongs to the space for any , provided the matrix of coefficients (Aij) has L ∞ ∩ VMO entries.

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