Mathematical Research Letters

Volume 1, Issue 1, January 1994 pp. 35-43.

Noyau de la chaleur d'opérateurs elliptiques complexes

Authors: Pascal Auscher, Alan McIntosh, and Philippe Tchamitchian
Author institution: Université de Rennes I, Macquarie University, and Faculté des Sciences and Techniques de Saint Jérome

Summary: 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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