Regularity and stochastic homogenization of fully nonlinear equations without uniform ellipticity.

Job Candidate Talk
Tuesday, November 20, 2012 - 11:05am for 1 hour (actually 50 minutes)
Skiles 006
Charles Smart – MIT
Andrzej Swiech
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.