no. 4
Partial differential equations/Probability theory
A Schauder estimate for stochastic PDEs
[Une estimée de Schauder pour des EDPs stochastiques]

Présenté par : the Editorial Board

Du, Kai1 ; Liu, Jiakun1
1 Institute for Mathematics and its Applications, School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia
Comptes Rendus. Mathématique, Tome 354 (2016) no. 4, pp. 371-375.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.01.010
Du, Kai 1 ; Liu, Jiakun 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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Du, Kai; Liu, Jiakun. A Schauder estimate for stochastic PDEs. Comptes Rendus. Mathématique, Tome 354 (2016) no. 4, pp. 371-375. doi : 10.1016/j.crma.2016.01.010. http://www.numdam.org/articles/10.1016/j.crma.2016.01.010/

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