Pseudo-differential operators and maximal regularity results for non-autonomous parabolic equations

Matthias Georg Hieber, Sylvie Monniaux

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

In this paper, we show that a pseudo-differential operator associated to a symbol a ε L(ℝ × ℝ, L(H)) (H being a Hubert space) which admits a holomorphic extension to a suitable sector of ℂ acts as a bounded operator on L2(ℝ, H). By showing that maximal Lp-regularity for the nonautonomous parabolic equation u′(t)+A(t)u(t) = f(t), u(0) = 0 is independent of p ε (1, ∞), we obtain as a consequence a maximal Lp([0, T], H)-regularity result for solutions of the above equation.

Original languageEnglish
Pages (from-to)1047-1053
Number of pages7
JournalProceedings of the American Mathematical Society
Volume128
Issue number4
Publication statusPublished - 2000
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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