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CATEGORIES:Geometric Analysis and Partial Differential Equati
ons seminar
SUMMARY:Quantitative estimates in stochastic homogenizatio
n - Daniel Marahrens (Max-Planck-Institute\, Leipz
ig)
DTSTART;TZID=Europe/London:20130213T150000
DTEND;TZID=Europe/London:20130213T160000
UID:TALK43268AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/43268
DESCRIPTION:Consider a discrete elliptic equation on the integ
er lattice with random coefficients\, arising for
example as the steady state of a diffusion through
the lattice with random diffusivities. Classical
homogenization results show that with ergodic coef
ficients and on large scales\, the solutions behav
e as the solutions to a diffusion equation with co
nstant homogenized coefficients. The homogenized c
oefficients can be characterised through the solut
ion to a so-called "corrector problem". In contras
t to periodic homogenization\, the stochastic homo
genization lacks compactness which makes the probl
em harder. Recently Gloria\, Otto and Neukamm have
developed tools to obtain optimal estimates for t
he homogenization and the corrector problem via a
spectral gap inequality. In this talk\, I will pre
sent how to obtain strong quantitative (optimal) e
stimates on the discrete Green's function via a lo
garithmic Sobolev inequality and consequences from
these estimates for the solutions to the discrete
equation. This is joint work with Felix Otto.
LOCATION:CMS\, MR11
CONTACT:Prof. ClĂ©ment Mouhot
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