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arXiv · 1312.3557

An extension of H\"{o}rmander's hypoellipticity theorem

David P. Herzog·Nathan Totz
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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.

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David P. Herzog, Nathan Totz. 2013-12-12. An extension of H\"{o}rmander's hypoellipticity theorem. https://arxiv.org/abs/1312.3557

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