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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Lp Estimates
Analytic Semigroup
Heat Kernel
A Priori Estimates
Commutator
Initial Value Problem
Semigroup
Generator
kernel

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Noyaux de la chaleur et estimations mixtes Lp - Lq optimales : Le cas non autonome. / Hieber, Matthias Georg; Monniaux, Sylvie.

In: Comptes Rendus de l'Academie des Sciences - Series I: Mathematics, Vol. 328, No. 3, 02.1999, p. 233-238.

Research output: Contribution to journalArticle

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