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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Neeb, Karl-Hermann / Noguchi, Junjiro / Shahidi, Freydoon / Sogge, Christopher D. / Wienhard, Anna


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1435-5337
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Regularity results for the gradient of solutions of linear elliptic systems with VMO-coefficients and L 1,λ data

Salvatore Leonardi1 / Jana Stará2

1Dipartimento di Matematica ed Informatica, Università di Catania, Viale A. Doria 6, 95125 Catania, Italy.

2Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic.

Citation Information: Forum Mathematicum. Volume 22, Issue 5, Pages 913–940, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/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.

Citing Articles

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[1]
S. Leonardi
Nonlinear Analysis: Theory, Methods & Applications, 2014, Volume 95, Page 530
[2]
S. Leonardi and J. Stará
Nonlinear Analysis: Theory, Methods & Applications, 2012, Volume 75, Number 4, Page 2069
[3]
Giuseppe Mingione
Milan Journal of Mathematics, 2011, Volume 79, Number 2, Page 429
[4]
S. Leonardi and J. Stará
Complex Variables and Elliptic Equations, 2011, Volume 56, Number 12, Page 1085
[5]
S. Leonardi
Nonlinear Differential Equations and Applications NoDEA, 2011, Volume 18, Number 3, Page 237

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