Integrated semigroups and the cauchy problem for systems in Lp spaces

Matthias Georg Hieber

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

In this note we prove that (under suitable hypotheses) every homogeneous differential operator on Lp(Rn)N, corresponding to a system which is well-posed in L2(Rn)N, generates an α-times integrated semigroup on Lp(Rn)N (1 <p <∞) whenever α > n | 1 2 - 1 p|. For some special systems of mathematical physics, such as the wave equation or Maxwell's equations this constant can be improved to be (n - 1) | 1 2 - 1 p|.

Original languageEnglish
Pages (from-to)300-308
Number of pages9
JournalJournal of Mathematical Analysis and Applications
Volume162
Issue number1
DOIs
Publication statusPublished - 1991 Nov 15
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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