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Maximal regularity with temporal weights for parabolic problems with inhomogeneous boundary conditions
Author(s) -
Meyries Martin,
Schnaubelt Roland
Publication year - 2012
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201100057
Subject(s) - mathematics , smoothing , boundary value problem , mathematical analysis , perturbation (astronomy) , compatibility (geochemistry) , anisotropy , interpolation (computer graphics) , physics , geochemistry , quantum mechanics , geology , animation , computer graphics (images) , computer science , statistics
We develop a maximal regularity approach in temporally weighted L p ‐spaces for vector‐valued parabolic initial‐boundary value problems with inhomogeneous boundary conditions, both of static and of relaxation type. Normal ellipticity and conditions of Lopatinskii‐Shapiro type are the basic structural assumptions. The weighted framework allows to reduce the initial regularity and to avoid compatibility conditions at the boundary, and it provides an inherent smoothing effect of the solutions. Our main tools are interpolation and trace theory for anisotropic Slobodetskii spaces with temporal weights, operator‐valued functional calculus, as well as localization and perturbation arguments.