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| HAL : hal-00674445, version 2 |
| DOI : 10.1080/03605302.2012.715319 |
| Fiche détaillée |  Récupérer au format |
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| Communications in Partial Differential Equations (2013) 1 |
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| Versions disponibles : | v1 (27-02-2012) | v2 (20-07-2012) |
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| Fluctuation of solutions to linear elliptic equations with noisy diffusion coefficients |
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| Antoine Gloria 1 |
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| (2013) |
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| 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. |
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| 1 : | SIMPAF (INRIA Lille - Nord Europe) |
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INRIA – Université Lille I - Sciences et technologies – CNRS : UMR |
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| SIMPAF |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles Mathématiques/Probabilités |
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| quantification of uncertainty – fluctuation – stochastic perturbation – variance estimate – stochastic homogenization. |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00674445, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00674445 | |
| oai:hal.archives-ouvertes.fr:hal-00674445 | |
| Contributeur : Antoine Gloria | |
| Soumis le : Vendredi 20 Juillet 2012, 14:33:09 | |
| Dernière modification le : Mercredi 19 Décembre 2012, 13:04:51 | |
