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

A. O. Caruso

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

Analysis of PDEs 2013-04-23 v1

Authors: A. O. Caruso

Abstract

We consider a divergence form hypoelliptic operator consisting of a system of real smooth vector fields $X_{1},..., X_{q}$ satisfying H\"ormander condition in some domain $\Omega\subseteq\erren$ . 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.

Keywords

operator theory and elliptic operators gradient estimates weighted inequalities

Cite

@article{arxiv.1304.5882,
  title  = {$W^{1,p}_{X}$ interior estimates for variational hypoelliptic operator with $VMO_X$ coefficients},
  author = {A. O. Caruso},
  journal= {arXiv preprint arXiv:1304.5882},
  year   = {2013}
}

Comments

Preliminary draft of the paper, with detailed sketch of the proof

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