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

- Series
- Job Candidate Talk
- Time
- Tuesday, November 20, 2012 - 11:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Charles Smart – MIT

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.