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Journal of the London Mathematical Society 1995 52(3):583-593; doi:10.1112/jlms/52.3.583
© 1995 by London Mathematical Society
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© The London Mathematical Society

Contractivity Properties of Schrödinger Semigroups on Bounded Domains

Fabio Cipriani and Gabriele Grillo

Ruhr-Universität Bochum, Universitätstrasse 150 4630 Bochum 1, Germany
Dipartimento di Matematica e Informatica, Università di Udine via Zanon 6, 33100 Udine, Italy

Received 4 January 1994. Revision received 19 May 1994.

We study intrinsic ultracontractivity (IUC) for the Schrödinger operator H = –{Delta} + V with Dirichlet boundary conditions on bounded domains ohm in Rn. The potential is not assumed either to belong to the Kato class, or to be relatively form-bounded with respect to the Dirichlet Laplacian on ohm. The class of domains considered includes John domains and a class of Hölder domains. We also give an example of a bounded domain ohm on which the Dirichlet Laplacian is not IUC, but on which –{Delta} + V is IUC for a suitable potential V.


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