Quantitative results in stochastic homogenization

Datum

13.06.2013

Zeit

15:15 - 16:15

Sprecher

Dr. Stefan Neukamm

Zugehörigkeit

Weierstrass Institut Berlin

Serie

TUD Mathematik Oberseminar Analysis

Sprache

en

Hauptthema

Mathematik

Andere Themen

Mathematik

Host

Dr. M. Waurick

Beschreibung

I will present recent quantitative results for the stochastic homogenization of linear elliptic equations with random coefficients in a discrete setting. Classical qualitative homogenization theory states that on large length scales the random coefficients can be replaced by homogenized coefficients that are deterministic and constant in space. The homogenized coefficients are characterized by a formula that involves the solution to the so called "corrector problem". In contrast to periodic homogenization, in the stochastic setting the corrector problem is a highly degenerate elliptic equation on a probability space.. In this talk I will explain how to obtain various optimal estimates on the corrector, on approximations of the homogenized coefficients and on the homogenization error based on quantification of ergodicity that in particular covers the case of independent and identically distributed coefficients. The approach is mainly based on elliptic and parabolic regularity theory combined with some elements of statistical mechanics and probability theory. The talk is based on joint work with A. Gloria (Université Libre de Bruxelles) and F. Otto (MPI Leipzig).

Links

• Webseite zum Oberseminar Analysis

Letztmalig verändert: 30.05.2013, 12:46:56