Higher differentiability for solutions of linearelliptic systems with measure data
Giuseppa Rita Cirmi, Salvatore Leonardi · Discrete and Continuous Dynamical Systems · 2009
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.