Abstract for the talk at 30.10.2012 (15:15 h)

Oberseminar ANALYSIS
Scott Armstrong (CNRS, Paris)
Regularity of degenerate elliptic equations in nondivergence form on large scales
I will present a regularity result for degenerate elliptic equations in nondivergence form. In joint work with Charlie Smart, we prove a Harnack inequality for equations with possibly unbounded ellipticity– provided that the ellipticity belongs to L^d (where d is the dimension). As an application we obtain a stochastic homogenization result for such equations (and a new estimate for the effective coefficients) as well as an invariance principle for random diffusions in random environments.