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arXiv · 1304.5882

$W^{1,p}_{X}$ interior estimates for variational hypoelliptic operator with $VMO_X$ coefficients

A. O. Caruso
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Abstract

We consider a divergence form hypoelliptic operator consisting of a system of real smooth vector fields $X_{1},..., X_{q}$ satisfying Hörmander condition in some domain $Ω\subseteq\erren$. Interior $L^{p}$ estimates, $2\leq p<\infty$, can be obtained for weak solutions of the equation $X_j^T(a^{ij}X_iu)=X_j^T F^j,$ by assuming that the coefficients $a^{ij}$ belong locally to the space $VMO_X$ with respect to the Carnot--Caratheodory metric induced by the vector fields.

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A. O. Caruso. 2013-04-22. $W^{1,p}_{X}$ interior estimates for variational hypoelliptic operator with $VMO_X$ coefficients. https://arxiv.org/abs/1304.5882

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