On the maximal L
p
-regularity of parabolic mixed-order systems |
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Authors: | Robert Denk J?rg Seiler |
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Institution: | 1. Fachbereich Mathematik und Statistik, Universit?t Konstanz, 78457, Konstanz, Germany 2. Department of Mathematical Sciences, Loughborough University, Leicestershire, LE11 3TU, UK
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Abstract: | We study maximal L
p
-regularity for a class of pseudodifferential mixed-order systems on a space–time cylinder
\mathbbRn ×\mathbbR{\mathbb{R}^n \times \mathbb{R}} or
X ×\mathbbR{X \times \mathbb{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 L
p
-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. |
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Keywords: | |
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