An extension of Hörmander's hypoellipticity theorem

2013/12/12 by David P. Herzog, Herzog, David P., Nathan Totz +1
Economics, Econometrics and Finance · Mathematics · #35-Partial Differential Equations #60-Probability Theory and Stochastic Processes #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1312.3557

openalex publication_date 2013/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motivated by applications to stochastic differential equations, an extension of Hörmander'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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