Maximal regularity with temporal weights for parabolic problems with inhomogeneous boundary conditions

2012/02/17 by Martin Meyries, Meyries, Martin, Roland Schnaubelt +1
Mathematics · #Advanced Mathematical Physics Problems #Advanced Harmonic Analysis Research #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1202.3875

Abstract

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.

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