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Keywords:
elliptic systems; Morrey space regularity; Carnot-Carathéodory metric
elliptic systems; Morrey space regularity; Carnot-Carathéodory metric
Summary:
Let $X=(X_1,X_2,\dots ,X_q)$ be a system of vector fields satisfying the Hör\-man\-der condition. We prove $L^{2,\lambda}_X$ local regularity for the gradient $Xu$ of a solution of the following strongly elliptic system $$ -X^{*}_{\alpha }(a^{\alpha \beta }_{ij}(x)X_{\beta } u^{j})= g_{i}-X^{*}_{\alpha } f^{\alpha }_{i}(x) \quad \forall i=1,2,\dots ,N, $$ where $a^{\alpha \beta }_{ij}(x)$ are bounded functions and belong to Vanishing Mean Oscillation space.
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