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Elliptic operators with infinite-dimensional state spaces

Elliptic operators with infinite-dimensional state spaces Motivated by applications to problems from physics, we study elliptic operators with operator-valued coefficients acting on Banach-space-valued distributions. After giving a definition of ellipticity, normal ellipticity in particular, generalizing the classical concepts, we show that normally elliptic operators are negative generators of analytic semigroups on $ L_p({\Bbb R}^n, E) $ for 1 $ \leq p < \infty $ and on $ BUC({\Bbb R}^n, E) $ and $ C_0({\Bbb R}^n, E) $ , as well as on all Besov spaces of E-valued distributions on $ {\Bbb R}^n $ , where E is any Banach space. This is true under minimal regularity assumptions for the coefficients, thanks to a point-wise multiplier theorem for E-valued distributions proven in the appendix. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Evolution Equations Springer Journals

Elliptic operators with infinite-dimensional state spaces

Journal of Evolution Equations , Volume 1 (2) – Jun 1, 2001

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References (19)

Publisher
Springer Journals
Copyright
Copyright © 2001 by Birkhäuser Verlag Basel,
Subject
Mathematics; Analysis
ISSN
1424-3199
DOI
10.1007/PL00001367
Publisher site
See Article on Publisher Site

Abstract

Motivated by applications to problems from physics, we study elliptic operators with operator-valued coefficients acting on Banach-space-valued distributions. After giving a definition of ellipticity, normal ellipticity in particular, generalizing the classical concepts, we show that normally elliptic operators are negative generators of analytic semigroups on $ L_p({\Bbb R}^n, E) $ for 1 $ \leq p < \infty $ and on $ BUC({\Bbb R}^n, E) $ and $ C_0({\Bbb R}^n, E) $ , as well as on all Besov spaces of E-valued distributions on $ {\Bbb R}^n $ , where E is any Banach space. This is true under minimal regularity assumptions for the coefficients, thanks to a point-wise multiplier theorem for E-valued distributions proven in the appendix.

Journal

Journal of Evolution EquationsSpringer Journals

Published: Jun 1, 2001

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