[Régularité Hölder–Sobolev des solutions d'une classe d'E.D.P.S. dirigées par un bruit coloré]
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 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 and driven by a spatially colored noise defined from an L2(D)-valued Wiener process.
Accepté le :
Publié le :
Marta Sanz-Solé 1 ; Pierre-A. Vuillermot 2
@article{CRMATH_2002__334_10_869_0,
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},
}
TY - JOUR AU - Marta Sanz-Solé AU - Pierre-A. Vuillermot TI - Hölder–Sobolev regularity of solutions to a class of SPDE's driven by a spatially colored noise JO - Comptes Rendus. Mathématique PY - 2002 SP - 869 EP - 874 VL - 334 IS - 10 PB - Elsevier DO - 10.1016/S1631-073X(02)02359-2 LA - en ID - CRMATH_2002__334_10_869_0 ER -
%0 Journal Article %A Marta Sanz-Solé %A Pierre-A. Vuillermot %T Hölder–Sobolev regularity of solutions to a class of SPDE's driven by a spatially colored noise %J Comptes Rendus. Mathématique %D 2002 %P 869-874 %V 334 %N 10 %I Elsevier %R 10.1016/S1631-073X(02)02359-2 %G en %F CRMATH_2002__334_10_869_0
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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