An Extension of Hörmander’s Hypoellipticity Theorem

David P. Herzog, Nathan Totz

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)403-433
Number of pages31
JournalPotential Analysis
Volume42
Issue number2
DOIs
StatePublished - Jan 1 2014
Externally publishedYes

Fingerprint

Hypoellipticity
Degenerate Elliptic Operators
Kernel Estimate
Weighted Inequalities
Sobolev Inequality
Friedrich Wilhelm Bessel
Theorem
Stochastic Equations
Differential equation
First-order
Coefficient
Term
Operator

Keywords

  • Degenerate stochastic differential equations
  • Hypoellipticity
  • Hörmander’s theorem
  • Malliavin calculus
  • Pseudo-differential calculus

ASJC Scopus subject areas

  • Analysis

Cite this

An Extension of Hörmander’s Hypoellipticity Theorem. / Herzog, David P.; Totz, Nathan.

In: Potential Analysis, Vol. 42, No. 2, 01.01.2014, p. 403-433.

Research output: Contribution to journalArticle

Herzog, David P. ; Totz, Nathan. / An Extension of Hörmander’s Hypoellipticity Theorem. In: Potential Analysis. 2014 ; Vol. 42, No. 2. pp. 403-433.
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