Colloquium, Monday, Nov 12: Charles Smart (MIT)

Title: Regularity and stochastic homogenization of fully 
nonlinear equations without uniform ellipticity

Abstract:
I will discuss regularity of fully nonlinear elliptic 
equations when the usual uniform upper bound on the 
ellipticity is replaced by bound on its $L^d$ norm, 
where $d$ is the dimension of the ambient space. Our 
estimates refine the classical theory and require 
several new ideas that we believe are of independent 
interest. As an application, we prove homogenization 
for a class of stationary ergodic strictly elliptic equations.