Comptes Rendus
Partial differential equations/Probability theory
A Schauder estimate for stochastic PDEs
Comptes Rendus. Mathématique, Volume 354 (2016) no. 4, pp. 371-375.

Considering stochastic partial differential equations of parabolic type with random coefficients in vector-valued Hölder spaces, we establish a sharp Schauder theory. The existence and uniqueness of solutions to the Cauchy problem is obtained.

Nous considérons des équations aux dérivées partielles stochastiques, du type parabolique et à coefficients aléatoires dans des espaces de Hölder à valeurs vectorielles. Nous obtenons une estimée de Schauder optimale, puis nous utilisons cette estimée pour prouver l'existence et l'unicité de la solution du problème de Cauchy.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.01.010

Kai Du 1; Jiakun Liu 1

1 Institute for Mathematics and its Applications, School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia
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Kai Du; Jiakun Liu. A Schauder estimate for stochastic PDEs. Comptes Rendus. Mathématique, Volume 354 (2016) no. 4, pp. 371-375. doi : 10.1016/j.crma.2016.01.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.01.010/

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