hal-00674445, version 2
Fluctuation of solutions to linear elliptic equations with noisy diffusion coefficients
Communications in Partial Differential Equations (2013) 1
Résumé : We consider a linear elliptic equation in divergence form on a bounded domain (or on $\R^d$) in dimension $d\geq 2$, whose coefficients are perturbed by a stationary noise of correlation length $\e>0$. We give estimates on the fluctuation of the solution in function of the correlation length $\e$ of the noise, both in terms of strong $L^2$ and weak $L^1$ norms. This result can be seen as a quantification of the propagation of uncertainties in linear elliptic partial differential equations.
- 1 :
- INRIA – Université Lille I - Sciences et technologies – CNRS : UMR
- Domaine : Mathématiques/Equations aux dérivées partielles
Mathématiques/Probabilités - Mots-clés : quantification of uncertainty – fluctuation – stochastic perturbation – variance estimate – stochastic homogenization.
- Versions disponibles : v1 (27-02-2012) v2 (20-07-2012)
- hal-00674445, version 2
- http://hal.archives-ouvertes.fr/hal-00674445
- oai:hal.archives-ouvertes.fr:hal-00674445
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- Soumis le : Vendredi 20 Juillet 2012, 14:33:09
- Dernière modification le : Mercredi 19 Décembre 2012, 13:04:51
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