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Higher differentiability for solutions of linear elliptic systems with measure data

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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.

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


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