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2007 Maximal regularity for nonsmooth parabolic problems in Sobolev-Morrey spaces
J. A. Griepentrog
Adv. Differential Equations 12(9): 1031-1078 (2007).

Abstract

This text is devoted to maximal regularity results for second-order parabolic systems on Lipschitz domains of space dimension $n \ge 3$ with diagonal principal part, nonsmooth coefficients, and nonhomogeneous mixed boundary conditions. We show that the corresponding class of initial-value problems generates isomorphisms between two scales of Sobolev--Morrey spaces for solutions and right-hand sides introduced in the first part [12] of our presentation. The solutions depend smoothly on the data of the problem. Moreover, they are Hölder continuous in time and space up to the boundary for a certain range of Morrey exponents. Due to the complete continuity of embedding and trace maps these results remain true for a broad class of unbounded lower-order coefficients.

Citation

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J. A. Griepentrog. "Maximal regularity for nonsmooth parabolic problems in Sobolev-Morrey spaces." Adv. Differential Equations 12 (9) 1031 - 1078, 2007.

Information

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

zbMATH: 1157.35023
MathSciNet: MR2351837

Subjects:
Primary: 35K20
Secondary: 35D10, 35R05

Rights: Copyright © 2007 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.12 • No. 9 • 2007
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