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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 Mathematiques, Universite de Franche-Comte, F-25030 Besancon Cedex, FRANCE Current address: Abteilung Mathematik V, Universitaet Ulm, D-89069 Ulm, GERMANY
(2) Laboratoire de Mathematiques, Universite de Franche-Comte, F-25030 Besancon 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.

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