Hölder–Sobolev regularity of solutions to a class of SPDE's driven by a spatially colored noise
Comptes Rendus. Mathématique, Volume 334 (2002) no. 10, pp. 869-874.

In this Note we present new results regarding the equivalence, the existence and the joint space–time regularity properties of various notions of solution to a class of non-autonomous, semilinear, stochastic partial differential equations defined on a smooth, bounded, convex domain D d and driven by a spatially colored noise defined from an L2(D)-valued Wiener process.

Dans cette Note nous présentons des résultats nouveaux concernant l'équivalence, l'existence et la régularité spatio–temporelle conjointe de diverses notions de solution relatives à une classe d'équations aux dérivées partielles stochastiques semilinéaires non autonomes définies dans un ouvert régulier borné convexe D d et dirigées par un bruit coloré en la variable spatiale défini à partir d'un processus de Wiener à valeurs dans L2(D).

Received:
Accepted:
DOI: 10.1016/S1631-073X(02)02359-2
Sanz-Solé, Marta 1; Vuillermot 2

1 Facultat de matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain
2 I.E.C.N., Université Henri-Poincaré, Nancy 1, BP 239, 54506 Vandoeuvre-lès-Nancy cedex, France
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     title = {H\"older{\textendash}Sobolev regularity of solutions to a class of {SPDE's} driven by a spatially colored noise},
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Sanz-Solé, Marta; Vuillermot. Hölder–Sobolev regularity of solutions to a class of SPDE's driven by a spatially colored noise. Comptes Rendus. Mathématique, Volume 334 (2002) no. 10, pp. 869-874. doi : 10.1016/S1631-073X(02)02359-2. http://www.numdam.org/articles/10.1016/S1631-073X(02)02359-2/

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