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Journal of the London Mathematical Society 1996 54(2):284-296; doi:10.1112/jlms/54.2.284
© 1996 by London Mathematical Society
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© The London Mathematical Society

Regularity Theorems and Heat Kernel for Elliptic Operators

Pascal Auscher

CNRS, IRMAR, Université de Rennes I, Campus de Beaulieu 35042 Rennes Cedex, France

Received 12 December 1993. Revision received 21 October 1994.

We give a new proof of Aronson's upper gaussian bound on the heat kernel for parabolic equations with time-independent real measurable coefficients. This approach also gives gaussian bounds in the case of a complex perturbation of real coefficients and in the case of uniformly continuous and complex-valued coefficients.

This work was done while the author was visiting the Mathematics Department, Brown University, Providence, Rhode Island 02912, USA

New address: Faculté de mathématiques et d'informatique, Université de Picardie-Jules Verne, 33 rue Saint-Leu, 80039 Amiens Cedex 1, France E-mail: auscher{at}mathinfo.u_picardie.fr


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