Geodesic
On the regularity of abstract Cauchy problems and boundary value problems
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 9 (1998) no. 4, pp. 245-266 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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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. 
@article{RLIN_1998_9_9_4_a2,
     author = {Cl\'ement, Philippe and Guerre-Delabri\`ere, Sylvie},
     title = {On the regularity of abstract {Cauchy} problems and boundary value problems},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {245--266},
     year = {1998},
     volume = {Ser. 9, 9},
     number = {4},
     zbl = {0928.34042},
     mrnumber = {MR1722785},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_1998_9_9_4_a2/}
}
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Clément, Philippe; Guerre-Delabrière, Sylvie. On the regularity of abstract Cauchy problems and boundary value problems. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 9 (1998) no. 4, pp. 245-266. http://geodesic.mathdoc.fr/item/RLIN_1998_9_9_4_a2/