Journal of Operator Theory

Volume 38, Issue 1, Summer 1997 pp. 87-130.

Gaussian estimates for second order elliptic operators with boundary conditions

Authors: W. Arendt (1) and A.F.M ter Elst (2)
Author institution:(1) Laboratoire de Mathématiques, Université de Franche-Comté, F-25030 Besançon Cedex, FRANCE Current address: Abteilung Mathematik V, Universität Ulm, D-89069 Ulm, GERMANY
(2) Laboratoire de Mathématiques, Université de Franche-Comté, F-25030 Besançon Cedex, FRANCE Home institution: Dept. of Math. and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, THE NETHERLANDS

Summary: We prove Gaussian estimates for the kernel of the semigroup generated by a second order operator A in divergence form with real, not necessarily symmetric, second order coefficients on an open subset $\Omega$ of $\mathbb R^d$ satisfying various boundary conditions. Moreover, we show that $A + \omegaI$ has a bounded $H_\infty$-functional calculus and has bounded imaginary powers if $\omega$ is large enough.

Keywords: Gaussian bounds, elliptic operators, boundary conditions, non-symmetric operators, functional calculus, bounded imaginary powers.

Contents Full-Text PDF