Interpolation, embeddings and traces of anisotropic fractional Sobolev spaces with temporal weights

2012/02/17 by Martin Meyries, Meyries, Martin, Roland Schnaubelt +1 · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Differential Equations and Boundary Problems #math.FA #msc:46E35 #msc:47A60

paper · pdf · doi:10.48550/arxiv.1202.3870

This is a preprint version. Published in Journal of Functional Analysis 262 (2012) 1200-1229

arxiv created 2012/02/17 · arxiv updated 2012/02/20

Abstract

We investigate the properties of a class of weighted vector-valued L_p-spaces and the corresponding (an)isotropic Sobolev-Slobodetskii spaces. These spaces arise naturally in the context of maximal L_p-regularity for parabolic initial-boundary value problems. Our main tools are operators with a bounded \calH^∞-calculus, interpolation theory, and operator sums.

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• Local well-posedness of the equations governing the motion of a fluid-filled elastic solid

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