Noyaux de la chaleur et estimations mixtes Lp - Lq optimales: Le cas non autonome

Translated title of the contribution: Heat kernel and maximal Lp - Lq estimates: The non-autonomous case

Matthias Georg Hieber, Sylvie Monniaux

Research output: Contribution to journalArticle

Abstract

Consider the non-autonomous initial value problem u′(t) + A(t)u(t) = f(t), u(0) = 0, where -A(t) is for each t ∈ [0,T], the generator of a bounded analytic semigroup on L2(Ω). We prove maximal Lp - Lq a priori estimates for the solution of the above equation provided the semigroups Tt are associated to kernels which satisfies an upper Gaussian bound and {A(t),t ∈[0,T]} fulfills a Acquistapace-Terreni commutator condition.

Original languageFrench
Pages (from-to)233-238
Number of pages6
JournalComptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume328
Issue number3
Publication statusPublished - 1999 Feb
Externally publishedYes

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ASJC Scopus subject areas

  • Mathematics(all)

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