COMPLEMENTS OF ADVANCED ANALYSIS
Learning outcomes of the course unit
The aim of the course is to describe some recent developments in random recent results used to study linear elleptic equations.
Course contents summary
During the first part of the course we shall prove a quantitative rate of homogenization with very good stochastic integrability. Next, we will develop a stochastic regularity theory (where theories of De Giorgi and Stampacchia play crucial role) and finally use this regularity theory to accelerate the rate of convergence of homogenization, and to boot strap it to the optimal one given by the Central Limit Theorem scaling.
The aim of the course is to describe some recent developments in random homogenization. The main focus in linea elliptic equations with random coefficients.
Assessment methods and criteria