Title :

Annealed estimates on the Green functions and uncertainty quantification

Author(s) :

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

Journal title :

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

Pages :

1153--1197

Publisher :

EMS

Publication date :

2016

ISSN :

0294-1449

HAL domain(s) :

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

English abstract : [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 ...
Show more >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).Show less >

Language :

Anglais

Popular science :

Non

European Project :

QUANTHOM

Comment :

43 pages

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL