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

Matthias Georg Hieber; Sylvie Monniaux

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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 L^p - L^q a priori estimates for the solution of the above equation provided the semigroups T_t are associated to kernels which satisfies an upper Gaussian bound and {A(t),t ∈[0,T]} fulfills a Acquistapace-Terreni commutator condition.

Translated title of the contribution	Heat kernel and maximal Lp - Lq estimates: The non-autonomous case
Original language	French
Pages (from-to)	233-238
Number of pages	6
Journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	328
Issue number	3
Publication status	Published - 1999 Feb
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

Cite this

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N2 - 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.

AB - 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.

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

Abstract

ASJC Scopus subject areas

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