Heat kernels and maximal Lp-Lq estimates for parabolic evolution equations

Matthias Georg Hieber; Jan Prüss

Heat kernels and maximal L^p-L^q estimates for parabolic evolution equations

Matthias Georg Hieber^*, Jan Prüss

^*Corresponding author for this work

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

220 Citations (Scopus)

Abstract

Let A be the generator of an analytic semigroup T on L²(Ω), where Ω is a homogeneous space with doubling property. We prove maximal L^p - L^q a-priori estimates for the solution of the parabolic evolution equation u′(t) = Au(t) + f(t), u(0) = 0 provided T may be represented by a heat-kernel satisfying certain bounds (and in particular a Gaussian bound).

Original language	English
Pages (from-to)	1647-1669
Number of pages	23
Journal	Communications in Partial Differential Equations
Volume	22
Issue number	9-10
Publication status	Published - 1997
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)
Analysis
Applied Mathematics

Cite this

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title = "Heat kernels and maximal Lp-Lq estimates for parabolic evolution equations",

abstract = "Let A be the generator of an analytic semigroup T on L2(Ω), where Ω is a homogeneous space with doubling property. We prove maximal Lp - Lq a-priori estimates for the solution of the parabolic evolution equation u′(t) = Au(t) + f(t), u(0) = 0 provided T may be represented by a heat-kernel satisfying certain bounds (and in particular a Gaussian bound).",

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year = "1997",

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T1 - Heat kernels and maximal Lp-Lq estimates for parabolic evolution equations

AU - Hieber, Matthias Georg

AU - Prüss, Jan

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N2 - Let A be the generator of an analytic semigroup T on L2(Ω), where Ω is a homogeneous space with doubling property. We prove maximal Lp - Lq a-priori estimates for the solution of the parabolic evolution equation u′(t) = Au(t) + f(t), u(0) = 0 provided T may be represented by a heat-kernel satisfying certain bounds (and in particular a Gaussian bound).

AB - Let A be the generator of an analytic semigroup T on L2(Ω), where Ω is a homogeneous space with doubling property. We prove maximal Lp - Lq a-priori estimates for the solution of the parabolic evolution equation u′(t) = Au(t) + f(t), u(0) = 0 provided T may be represented by a heat-kernel satisfying certain bounds (and in particular a Gaussian bound).

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M3 - Article

AN - SCOPUS:0001098734

SN - 0360-5302

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JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

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ER -

Heat kernels and maximal L^p-L^q estimates for parabolic evolution equations

Abstract

ASJC Scopus subject areas

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