Integrated semigroups and the cauchy problem for systems in Lp spaces

Matthias Georg Hieber

doi:10.1016/0022-247X(91)90196-7

Integrated semigroups and the cauchy problem for systems in L^p spaces

Matthias Georg Hieber^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

In this note we prove that (under suitable hypotheses) every homogeneous differential operator on L^p(Rⁿ)^N, corresponding to a system which is well-posed in L²(Rⁿ)^N, generates an α-times integrated semigroup on L^p(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 language	English
Pages (from-to)	300-308
Number of pages	9
Journal	Journal of Mathematical Analysis and Applications
Volume	162
Issue number	1
DOIs	https://doi.org/10.1016/0022-247X(91)90196-7
Publication status	Published - 1991 Nov 15
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

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AB - 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 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|.

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Integrated semigroups and the cauchy problem for systems in L^p spaces

Abstract

ASJC Scopus subject areas

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