EVENT DETAILS AND ABSTRACT

Title: Homogenization of Oscillating Boundary Data
Speaker: William Feldman
Speaker Info: University of Chicago
Brief Description:
Special Note:
Abstract:

We will discuss the homogenization of periodic oscillating Dirichlet boundary data problems in general domains for second order elliptic equations. These problems are connected with the study of boundary layers in fluid mechanics and with the study of higher order asymptotic expansions in classical homogenization theory. The talk will be aimed at a general audience. Due to a singular behavior of the averaging near boundary points with rational normal direction the regularity of the limiting problem has so far not been well understand. We will explain some progress on this issue which displays a sharp contrast between the case of linear and nonlinear equations. In the linear case we establish continuity estimates, while in the nonlinear case we show that discontinuity is a generic phenomenon. This talk is based on joint work with Inwon Kim.