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

Research output: Contribution to journalArticle

152 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 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).

Original languageEnglish
Pages (from-to)1647-1669
Number of pages23
JournalCommunications in Partial Differential Equations
Volume22
Issue number9-10
Publication statusPublished - 1997
Externally publishedYes

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Lp Estimates
Heat Kernel
Parabolic Equation
Evolution Equation
Analytic Semigroup
Doubling
Homogeneous Space
A Priori Estimates
Generator
Hot Temperature

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis
  • Applied Mathematics

Cite this

Heat kernels and maximal Lp-Lq estimates for parabolic evolution equations. / Hieber, Matthias Georg; Prüss, Jan.

In: Communications in Partial Differential Equations, Vol. 22, No. 9-10, 1997, p. 1647-1669.

Research output: Contribution to journalArticle

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