Harnack inequality for hypoelliptic second order partial differential operators
Analysis of PDEs
2015-09-18 v1
Abstract
We consider nonnegative solutions of second order hypoelliptic equations \begin{equation*} \mathscr{L} u(x) =\sum_{i,j=1}^n \partial_{x_i} \left(a_{ij}(x)\partial_{x_j} u(x) \right) + \sum_{i=1}^n b_i(x) \partial_{x_i} u(x) =0, \end{equation*} where is a bounded open subset of and denotes the point of . For any fixed , we prove a Harnack inequality of this type where is any compact subset of the interior of the -propagation set of and the constant does not depend on .
Cite
@article{arxiv.1509.05245,
title = {Harnack inequality for hypoelliptic second order partial differential operators},
author = {Alessia E. Kogoj and Sergio Polidoro},
journal= {arXiv preprint arXiv:1509.05245},
year = {2015}
}