Titre :

Annealed estimates on the Green functions and uncertainty quantification

Auteur(s) :

Gloria, Antoine [Auteur]
Quantitative methods for stochastic models in physics [MEPHYSTO]
Département de Mathématique [Bruxelles] [ULB]
Marahrens, Daniel [Auteur]
Max-Planck-Institut für Mathematik in den Naturwissenschaften [MPI-MiS]

Titre de la revue :

Annales de l'Institut Henri Poincaré C, Analyse non linéaire

Pagination :

1153--1197

Éditeur :

EMS

Date de publication :

2016

ISSN :

0294-1449

Discipline(s) HAL :

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

Résumé en anglais : [en]

We prove optimal annealed decay estimates on the derivative and mixed second derivative of the elliptic Green functions on $\mathbb{R}^d$ for random stationary measurable coefficients that satisfy a certain logarithmic ...
Lire la suite >We prove optimal annealed decay estimates on the derivative and mixed second derivative of the elliptic Green functions on $\mathbb{R}^d$ for random stationary measurable coefficients that satisfy a certain logarithmic Sobolev inequality and for periodic coefficients, extending to the continuum setting results by Otto and the second author for discrete elliptic equations. As a main application we obtain optimal estimates on the fluctuations of solutions of linear elliptic PDEs with "noisy" diffusion coefficients, an uncertainty quantification result. As a direct corollary of the decay estimates we also prove that for these classes of coefficients the H\"older exponent of the celebrated De Giorgi-Nash-Moser theory can be taken arbitrarily close to 1 in the large (that is, away from the singularity).Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Projet Européen :

QUANTHOM

Commentaire :

43 pages

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL