Clément, Philippe and Guerre-Delabrière, Sylvie:
On the regularity of abstract Cauchy problems and boundary value problems (Sulla regolarità di problemi di Cauchy astratti e di problemi al contorno)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni Serie 9 9 (1998), fasc. n.4, p. 245-266, (English)
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Sunto
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.
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