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ISSN 1079-6762

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

Author(s): Peter Weidemaier
Journal: Electron. Res. Announc. Amer. Math. Soc. 8 (2002), 47-51.
MSC (2000): Primary 35K20, 46E35; Secondary 26D99
Posted: 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 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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