Mathematical Research Letters

Volume 1 (1994)

Number 1

Noyau de la chaleur d'opérateurs elliptiques complexes

Pages: 35 – 43

DOI: http://dx.doi.org/10.4310/MRL.1994.v1.n1.a4

Authors

Pascal Auscher (Université de Rennes I)

Alan McIntosh (Macquarie University)

Philippe Tchamitchian (Faculté des Sciences and Techniques de Saint Jérome)

Abstract

We study the heat kernel of second order elliptic operators in divergence form with complex non-smooth bounded coefficients on ${\Bbb{R}}^n$. We obtain Gaussian bounds without further assumption if $n \le 2$, and when the principal part has Hölder continuous coefficients if $n \ge 3$. Some applications are discussed.

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