Higher differentiability for solutions of  linearelliptic systems with measure  data

G. R. Cirmi; S. Leonardi

doi:10.3934/dcds.2010.26.89

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2010, Volume 26, Issue 1: 89-104. Doi: 10.3934/dcds.2010.26.89

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Higher differentiability for solutions of linear elliptic systems with measure data

G. R. Cirmi^1, and
S. Leonardi^1,

1.
Dipartimento di Matematica ed Informatica, Universitá degli Studi di Catania, Viale A. Doria 6 - 95125 Catania

Received: December 31, 2008

Revised: July 31, 2009

Published: February 2010

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Abstract

We study the differentiability of the solution of the Dirichlet problem associated to the system

$A(u) \equiv - D_i (A_{ij}(x) D_j u) = \mu $
$u \in W^{1,1}_0$(Ω$, \IR^N)$

where Ω is an open bounded subset of $\IR^n$ $(n \geq 2)$ with $C^1$-boundary, $A$ is an elliptic operator with C^{0, α}-coefficients ($\alpha \in ]0,1]$) and $\mu$ is a signed Radon measure with finite total variation, satisfying a suitable density condition.

Keywords:

Elliptic systems,
Measure-data.

Mathematics Subject Classification: Primary: 35J57; Secondary: 35B65.

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