On the regularity of abstract Cauchy problems and boundary value problems

Clément, Philippe; Guerre-Delabrière, Sylvie

Clément, Philippe ; Guerre-Delabrière, Sylvie

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 9 (1998), p. 245-266 / Harvested from Biblioteca Digitale Italiana di Matematica

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Abstract
Résumé

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.

Viene studiata la regolarità massimale (in $L_{p}$ ) di problemi di Cauchy astratti di ordine uno e di problemi al contorno di ordine due. In generale, la regolarità del primo tipo di problemi implica la regolarità del secondo; l’inverso viene dimostrato quando lo spazio di Banach in oggetto ha la proprietà UMD. Una nozione di regolarità forte, introdotta da Sobolevskii, ha un ruolo importante nelle dimostrazioni.

Publié le : 1998-12-01

MR 1722785 | Zbl 0928.34042

@article{RLIN_1998_9_9_4_245_0,
     author = {Philippe Cl\'ement and Sylvie Guerre-Delabri\`ere},
     title = {On the regularity of abstract Cauchy problems and boundary value problems},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {9},
     year = {1998},
     pages = {245-266},
     zbl = {0928.34042},
     mrnumber = {1722785},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_1998_9_9_4_245_0}
}

Clément, Philippe; 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, Tome 9 (1998) pp. 245-266. http://gdmltest.u-ga.fr/item/RLIN_1998_9_9_4_245_0/

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