On the maximal Lp-regularity of parabolic mixed order systems

2010
Series
Konstanzer Schriften in Mathematik; 266
Publication type
Working Paper/Technical Report
Abstract
We study maximal Lp-regularity for a class of pseudodifferential mixed order systems on a space-time cylinder ℝn x ℝ or X x ℝ where X is a closed smooth manifold. To this end we construct a calculus of Volterra pseudodifferential operators and characterize the parabolicity of a system by the invertibility of certain associated symbols. A parabolic system is shown to induce isomorphisms between suitable Lp-Sobolev spaces of Bessel potential or Besov type. If the cross section of the space-time cylinder is compact, the inverse of a parabolic system belongs to the calculus again. As applications we discuss time-dependent Douglis-Nirenberg systems and a linear system arising in the study of the Stefan problem with Gibbs-Thomson correction.
510 Mathematics
Keywords
Pseudodifferentialoperatoren,Systeme gemischter Ordnung,maximale Regularität,Pseudodifferential operators,mixed-order systems,maximal regularity
Cite This
ISO 690DENK, Robert, Jörg SEILER, 2010. On the maximal Lp-regularity of parabolic mixed order systems
BibTex
@techreport{Denk2010maxim-568,
year={2010},
series={Konstanzer Schriften in Mathematik},
title={On the maximal Lp-regularity of parabolic mixed order systems},
number={266},
author={Denk, Robert and Seiler, Jörg}
}

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Yes