Heat-Kernels and Maximal LP-Lq-Estimates: The Non-Autonomous Case

Matthias Georg Hieber, Sylvie Monniaux

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6 Citations (Scopus)

Abstract

In this paper, we establish maximal Lp-Lq estimates for non-autonomous parabolic equations of the type u′(t) + A(t)u(t) = f(t), u(0) = 0 under suitable conditions on the kernels of the semigroups generated by the operators -A(t), t ∈ [0, T]. We apply this result on semilinear problems of the form u′(t) + A(t)u(t) = f(t, u(t)), u(0) = 0.

Original languageEnglish
Pages (from-to)467-481
Number of pages15
JournalJournal of Knot Theory and its Ramifications
Volume6
Issue number5
Publication statusPublished - 2000
Externally publishedYes

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Keywords

  • Heat-kernel estimates
  • Maximal l - L-regularity
  • Non-autonomous cauchy problem
  • Singular integrals

ASJC Scopus subject areas

  • Algebra and Number Theory

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