Geodesic
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. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 7 (1996) no. 3, pp. 161-168

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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 \( C^{2 + \theta} (\overline{\Omega}) \) (0 \theta 1), with \( \partial_{t} u \) bounded with values in \( C^{\theta} (\overline{\Omega}) \). 
@article{RLIN_1996_9_7_3_a4,
     author = {Guidetti, Davide},
     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. Rendiconti Lincei. Matematica e applicazioni},
     pages = {161--168},
     publisher = {mathdoc},
     volume = {Ser. 9, 7},
     number = {3},
     year = {1996},
     zbl = {0871.35045},
     mrnumber = {MR1454411},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_1996_9_7_3_a4/}
}
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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. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 7 (1996) no. 3, pp. 161-168. http://geodesic.mathdoc.fr/item/RLIN_1996_9_7_3_a4/