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

Matthias Georg Hieber*, Sylvie Monniaux

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


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
Issue number5
Publication statusPublished - 2000
Externally publishedYes


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

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics
  • Analysis


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