Title :

Fluctuation of solutions to linear elliptic equations with noisy diffusion coefficients

Author(s) :

Gloria, Antoine [Auteur]
SImulations and Modeling for PArticles and Fluids [SIMPAF]

Journal title :

Communications in Partial Differential Equations

Pages :

35

Publisher :

Taylor & Francis

Publication date :

2013

ISSN :

0360-5302

English keyword(s) :

quantification of uncertainty
fluctuation
stochastic perturbation
variance estimate
stochastic homogenization.
stochastic homogenization

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Probabilités [math.PR]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL