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Proceedings of the American Mathematical Society

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Trace theorems for holomorphic semigroups
and the second order Cauchy problem

Authors: O. El-Mennaoui and V. Keyantuo
Journal: Proc. Amer. Math. Soc. 124 (1996), 1445-1458
MSC (1991): Primary 47D06, 47F05
MathSciNet review: 1301022
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Abstract: We use the theory of boundary values (also called traces) of holomorphic semigroups as developed by Boyadzhiev-deLaubenfels (1993) and El-Mennaoui (1992) to study the second order Cauchy problem for certain generators of holomorphic semigroups. Our results contain in particular the result of Hieber (Math. Ann. 291 (1991), 1--16) for the Laplace operator on $L^p(\mathbb R^N)$.

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Additional Information

O. El-Mennaoui
Affiliation: Mathematisches Institut der Universität Tübingen, Auf der Morgenstelle 10, 7400 Tübingen, Germany

V. Keyantuo
Affiliation: Équipe de Mathématiques, Université de Franche-Comté, Route de Gray, 25030 Besançon, France
Address at time of publication: Department of Mathematics, University of Puerto Rico, Box 23355 Rio Piedras, Puerto Rico 00931

Received by editor(s): June 6, 1994
Received by editor(s) in revised form: September 26, 1994
Additional Notes: This work was supported by the DAAD and the European Science Plan “Evolutionary Systems”.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society