Heat-kernels and maximal Lp - Lq estimates: The non-autonomous case

Matthias Georg Hieber, Sylvie Monniaux

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

In this paper, we establish maximal Lp-Lq estimates for rum-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 Fourier Analysis and Applications
Volume6
Issue number5
Publication statusPublished - 2000
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Analysis

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