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ISSN 1079-6762


Maximal regularity for parabolic equations with inhomogeneous boundary conditions in Sobolev spaces with mixed $L_p$-norm

Author: Peter Weidemaier
Journal: Electron. Res. Announc. Amer. Math. Soc. 8 (2002), 47-51
MSC (2000): Primary 35K20, 46E35; Secondary 26D99
Published electronically: December 19, 2002
MathSciNet review: 1945779
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Abstract: We determine the exact regularity of the trace of a function $ u \in L_{q}\,(0,T;\, W_{p}^{2}(\Omega)) $ $ \cap \, W^{1}_{q}\,(0,T;\, {L_{p}\,(\Omega))} $ and of the trace of its spatial gradient on $\partial \Omega \times (\,0,T\,) $ in the regime $ p \le q $. While for $ p=q $ both the spatial and temporal regularity of the traces can be completely characterized by fractional order Sobolev-Slobodetskii spaces, for $ p \neq q $ the Lizorkin-Triebel spaces turn out to be necessary for characterizing the sharp temporal regularity.

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Peter Weidemaier
Affiliation: Fraunhofer-Institut Kurzzeitdynamik, Eckerstr. 4, D-79104 Freiburg, Germany

PII: S 1079-6762(02)00104-X
Keywords: Maximal regularity, inhomogeneous boundary conditions, trace theory, mixed norm, Lizorkin-Triebel spaces
Received by editor(s): October 16, 2002
Published electronically: December 19, 2002
Communicated by: Michael E. Taylor
Article copyright: © Copyright 2002 American Mathematical Society