An extension of H\"{o}rmander's hypoellipticity theorem
Analysis of PDEs
2013-12-13 v1 Probability
Abstract
Motivated by applications to stochastic differential equations, an extension of H\"{o}rmander's hypoellipticity theorem is proved for second-order degenerate elliptic operators with non-smooth coefficients. The main results are established using point-wise Bessel kernel estimates and a weighted Sobolev inequality of Stein and Weiss. Of particular interest is that our results apply to operators with quite general first-order terms.
Keywords
Cite
@article{arxiv.1312.3557,
title = {An extension of H\"{o}rmander's hypoellipticity theorem},
author = {David P. Herzog and Nathan Totz},
journal= {arXiv preprint arXiv:1312.3557},
year = {2013}
}
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36 pages