On the regularity of abstract Cauchy problems and boundary value problems

Philippe Clément; Sylvie Guerre-Delabrière

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1998)

  • Volume: 9, Issue: 4, page 245-266
  • ISSN: 1120-6330

Abstract

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Maximal regularity (in L p -sense) for abstract Cauchy problems of order one and boundary value problems of order two is studied. In general, regularity of the first problems implies regularity of the second ones; the converse is shown to hold if the underlying Banach space has the UMD property. A stronger notion of regularity, introduced by Sobolevskii, plays an important role in the proofs.

How to cite

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Clément, Philippe, and Guerre-Delabrière, Sylvie. "On the regularity of abstract Cauchy problems and boundary value problems." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 9.4 (1998): 245-266. <http://eudml.org/doc/252392>.

@article{Clément1998,
abstract = {Maximal regularity (in \( L\_\{p\} \)-sense) for abstract Cauchy problems of order one and boundary value problems of order two is studied. In general, regularity of the first problems implies regularity of the second ones; the converse is shown to hold if the underlying Banach space has the UMD property. A stronger notion of regularity, introduced by Sobolevskii, plays an important role in the proofs.},
author = {Clément, Philippe, Guerre-Delabrière, Sylvie},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Abstract differential equations; UMD-spaces; Maximal regularity; abstract differential equations; maximal regularity; Cauchy problems; boundary value problems},
language = {eng},
month = {12},
number = {4},
pages = {245-266},
publisher = {Accademia Nazionale dei Lincei},
title = {On the regularity of abstract Cauchy problems and boundary value problems},
url = {http://eudml.org/doc/252392},
volume = {9},
year = {1998},
}

TY - JOUR
AU - Clément, Philippe
AU - Guerre-Delabrière, Sylvie
TI - On the regularity of abstract Cauchy problems and boundary value problems
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1998/12//
PB - Accademia Nazionale dei Lincei
VL - 9
IS - 4
SP - 245
EP - 266
AB - Maximal regularity (in \( L_{p} \)-sense) for abstract Cauchy problems of order one and boundary value problems of order two is studied. In general, regularity of the first problems implies regularity of the second ones; the converse is shown to hold if the underlying Banach space has the UMD property. A stronger notion of regularity, introduced by Sobolevskii, plays an important role in the proofs.
LA - eng
KW - Abstract differential equations; UMD-spaces; Maximal regularity; abstract differential equations; maximal regularity; Cauchy problems; boundary value problems
UR - http://eudml.org/doc/252392
ER -

References

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