### Abstract

In this note we prove that (under suitable hypotheses) every homogeneous differential operator on L^{p}(R^{n})^{N}, corresponding to a system which is well-posed in L^{2}(R^{n})^{N}, generates an α-times integrated semigroup on L^{p}(R^{n})^{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 |
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Pages (from-to) | 300-308 |

Number of pages | 9 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 162 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1991 Nov 15 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

**Integrated semigroups and the cauchy problem for systems in L ^{p} spaces.** / Hieber, Matthias Georg.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Integrated semigroups and the cauchy problem for systems in Lp spaces

AU - Hieber, Matthias Georg

PY - 1991/11/15

Y1 - 1991/11/15

N2 - 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|.

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|.

UR - http://www.scopus.com/inward/record.url?scp=0006045778&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0006045778&partnerID=8YFLogxK

U2 - 10.1016/0022-247X(91)90196-7

DO - 10.1016/0022-247X(91)90196-7

M3 - Article

AN - SCOPUS:0006045778

VL - 162

SP - 300

EP - 308

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -