Hölder–Sobolev regularity of solutions to a class of SPDE's driven by a spatially colored noise

Marta Sanz-Solé; Pierre-A. Vuillermot

doi:10.1016/S1631-073X(02)02359-2

Hölder–Sobolev regularity of solutions to a class of SPDE's driven by a spatially colored noise
[Régularité Hölder–Sobolev des solutions d'une classe d'E.D.P.S. dirigées par un bruit coloré]

Marta Sanz-Solé ¹ ; Pierre-A. 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

Comptes Rendus. Mathématique, Volume 334 (2002) no. 10, pp. 869-874.

Résumé
Abstract

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 $D \subset ℝ^{d}$ et dirigées par un bruit coloré en la variable spatiale défini à partir d'un processus de Wiener à valeurs dans L²(D).

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 $D \subset ℝ^{d}$ and driven by a spatially colored noise defined from an L²(D)-valued Wiener process.

Reçu le : 2002-01-31
Accepté le : 2002-03-15
Publié le : 2002-04-15

DOI : 10.1016/S1631-073X(02)02359-2

Affiliations des auteurs :

Marta Sanz-Solé ¹ ; Pierre-A. 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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     author = {Marta Sanz-Sol\'e and Pierre-A. Vuillermot},
     title = {H\"older{\textendash}Sobolev regularity of solutions to a class of {SPDE's} driven by a spatially colored noise},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {869--874},
     publisher = {Elsevier},
     volume = {334},
     number = {10},
     year = {2002},
     doi = {10.1016/S1631-073X(02)02359-2},
     language = {en},
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Marta Sanz-Solé; Pierre-A. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02359-2/

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Mark C. Veraar Non-autonomous stochastic evolution equations and applications to stochastic partial differential equations, Journal of Evolution Equations, Volume 10 (2010) no. 1, pp. 85-127 | DOI:10.1007/s00028-009-0041-7 | Zbl:1239.60062
I. D. Chueshov; P. A. Vuillermot Non-random invariant sets for some systems of parabolic stochastic partial differential equations, Stochastic Analysis and Applications, Volume 22 (2004) no. 6, pp. 1421-1486 | DOI:10.1081/sap-200029487 | Zbl:1065.60076

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