R-Boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type

Robert Denk, Matthias Georg Hieber, Jan Prüss

Research output: Contribution to journalArticle

458 Citations (Scopus)

Abstract

The property of maximal Lp-regularity for parabolic evolution equations is investigated via the concept of R-sectorial operators and operator-valued Fourier multipliers. As application, we consider the L q-realization of an elliptic boundary value problem of order 2m with operator-valued coefficients subject to general boundary conditions. We show that there is maximal Lp-Lq-regularity for the solution of the associated Cauchy problem provided the top order coefficients are bounded and uniformly continuous.

Original languageEnglish
JournalMemoirs of the American Mathematical Society
Issue number788
Publication statusPublished - 2003 Nov
Externally publishedYes

Keywords

  • Differential operators with operator-valued coefficients
  • L-theory for boundary value problems of general type
  • Lopatinskii-Shapiro condition
  • Maximal L-regularity
  • Operator-valued Fourier multipliers
  • R-boundedness

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'R-Boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type'. Together they form a unique fingerprint.

  • Cite this