Advanced Search

Let $X=(X_1,X_2,\cdots ,X_q)$ be a system of vector fields satisfying the Hörmander condition. We prove $L_X^{2,\lambda }$ local regularity for the gradient $Xu$ of a solution of the following strongly elliptic system $$-X_{\alpha }^{*}\left(a_{ij}^{\alpha \beta }\left(x\right)X_{\beta }{u}^j\right)=g_i-X_{\alpha }^{*}{f}_i^{\alpha }\left(x\right)\forall i=1,2,\cdots ,N,$$ where $a_{ij}^{\alpha \beta }\left(x\right)$ are bounded functions and belong to Vanishing Mean Oscillation space.