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2007 Sobolev-Morrey spaces associated with evolution equations
Jens A. Griepentrog
Adv. Differential Equations 12(7): 781-840 (2007).

Abstract

In this text we introduce new classes of Sobolev--Morrey spaces being adequate for the regularity theory of second-order parabolic boundary-value problems on Lipschitz domains of space dimension $n \ge 3$ with nonsmooth coefficients and mixed boundary conditions. We prove embedding and trace theorems as well as invariance properties of these spaces with respect to localization, Lipschitz transformation, and reflection. In the second part [11] of our presentation we show that the class of second-order parabolic systems with diagonal principal part generates isomorphisms between the above-mentioned Sobolev--Morrey spaces of solutions and right-hand sides.

Citation

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Jens A. Griepentrog. "Sobolev-Morrey spaces associated with evolution equations." Adv. Differential Equations 12 (7) 781 - 840, 2007.

Information

Published: 2007
First available in Project Euclid: 18 December 2012

zbMATH: 1157.35022
MathSciNet: MR2331524

Subjects:
Primary: 46E35
Secondary: 35K57, 35R20, 47N20

Rights: Copyright © 2007 Khayyam Publishing, Inc.

JOURNAL ARTICLE
60 PAGES


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Vol.12 • No. 7 • 2007
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