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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

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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