Archival Version
These pages are not updated anymore.
They reflect the state of
.
For the current production of this journal, please refer to
http://www.math.psu.edu/era/.
Maximal regularity for parabolic equations with inhomogeneous boundary conditions in Sobolev spaces with mixed $L_p$-norm
This journal is archived by the American Mathematical
Society. The master copy is available at
http://www.ams.org/era/
Maximal regularity for parabolic equations with inhomogeneous boundary conditions in Sobolev spaces with mixed $L_p$-norm
Peter Weidemaier
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.
Copyright 2002 American Mathematical Society
Retrieve entire article
Article Info
- ERA Amer. Math. Soc. 08 (2002), pp. 47-51
- Publisher Identifier: S 1079-6762(02)00104-X
- 2000 Mathematics Subject Classification. Primary 35K20, 46E35; Secondary 26D99
- Key words and phrases. Maximal regularity, inhomogeneous boundary conditions, trace theory, mixed norm, Lizorkin-Triebel spaces
- Received by editors October 16, 2002
- Posted on December 19, 2002
- Communicated by Michael E. Taylor
- Comments (When Available)
Peter Weidemaier
Fraunhofer-Institut Kurzzeitdynamik, Eckerstr. 4, D-79104 Freiburg, Germany
E-mail address: weide@emi.fhg.de
Electronic Research Announcements of the AMS Home page