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

Matthias Georg Hieber, Jan Prüss

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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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ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis
  • Applied Mathematics

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