Higher differentiability for solutions of linear elliptic systems with measure data

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January 2010, 26(1): 89-104. doi: 10.3934/dcds.2010.26.89

Higher differentiability for solutions of linear elliptic systems with measure data

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

Received January 2009 Revised August 2009 Published October 2009

Abstract
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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: Measure-data., Elliptic systems.

Mathematics Subject Classification: Primary: 35J57; Secondary: 35B6.

Citation: G. R. Cirmi, S. Leonardi. Higher differentiability for solutions of linear elliptic systems with measure data. Discrete & Continuous Dynamical Systems - A, 2010, 26 (1) : 89-104. doi: 10.3934/dcds.2010.26.89

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