Publikation:

On the maximal Lp-regularity of parabolic mixed order systems

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266_Denk_Seiler.pdf
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2010

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http://nbn-resolving.de/urn:nbn:de:bsz:352-opus-119246
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Zusammenfassung

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.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

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Pseudodifferentialoperatoren, Systeme gemischter Ordnung, maximale Regularität, Pseudodifferential operators, mixed-order systems, maximal regularity

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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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    <dcterms:abstract xml:lang="eng">We study maximal L&lt;sub&gt;p&lt;/sub&gt;-regularity for a class of pseudodifferential mixed order systems on a space-time cylinder &amp;#8477;&lt;sup&gt;n&lt;/sup&gt; x &amp;#8477; or X x &amp;#8477; 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&lt;sub&gt;p&lt;/sub&gt;-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.</dcterms:abstract>
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