The parabolic mixed Cauchy-Dirichlet problem in spaces of functions which are hölder continuous with respect to space variables
Guidetti, Davide
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 7 (1996), p. 161-168 / Harvested from Biblioteca Digitale Italiana di Matematica
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We give a new proof, based on analytic semigroup methods, of a maximal regularity result concerning the classical Cauchy-Dirichlet's boundary value problem for second order parabolic equations. More specifically, we find necessary and sufficient conditions on the data in order to have a strict solution u which is bounded with values in C2+θ⁢Ω¯ (0 < \theta < 1), with ∂t⁡u bounded with values in Cθ⁢Ω¯.

Si dà una nuova dimostrazione, basata su metodi di semigruppi analitici, di un risultato di regolarità massimale per il classico problema al contorno di Cauchy-Dirichlet per equazioni paraboliche del secondo ordine. Più specificamente, si trovano condizioni necessarie e sufficienti sui dati per avere una soluzione stretta u che sia limitata a valori in C2+θ⁢Ω¯ con ∂t⁡u limitata a valori in Cθ⁢Ω¯.

Publié le : 1996-12-01
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     author = {Davide Guidetti},
     title = {The parabolic mixed Cauchy-Dirichlet problem in spaces of functions which are h\"older continuous with respect to space variables},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {7},
     year = {1996},
     pages = {161-168},
     zbl = {0871.35045},
     mrnumber = {1454411},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_1996_9_7_3_161_0}
}

Guidetti, Davide. The parabolic mixed Cauchy-Dirichlet problem in spaces of functions which are hölder continuous with respect to space variables. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 7 (1996) pp. 161-168. http://gdmltest.u-ga.fr/item/RLIN_1996_9_7_3_161_0/

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