Abstract
We provide sharp estimates in Lorentz spaces for the solution of the Dirichlet problem associated to the system
where Ω is an open bounded subset of \({\mathbb R^n}\) (n ≥ 3) with sufficiently regular boundary, A(u) is an elliptic operator with VMO-coefficients and f is not in the natural dual space. Moreover, when the coefficients belong to \({{{C}^{0,\alpha}}(\alpha\in ]0,1[)}\), we study the differentiability of the solution in Besov–Morrey spaces.
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Leonardi, S. Gradient estimates below duality exponent for a class of linear elliptic systems. Nonlinear Differ. Equ. Appl. 18, 237–254 (2011). https://doi.org/10.1007/s00030-010-0093-y
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DOI: https://doi.org/10.1007/s00030-010-0093-y