Henrik Shahgholian: Surface integrals of rapidly oscillating functions, with applications to PDE

In this talk I will discuss the limit behavior of surface integrals of rapidly oscillating periodic functions. It turns out that the lower dimensional character of the surface gives rise to unexpected and surprising effective limit. A direct consequence of this integral averaging is homogenization of Dirichlet and related problems for operators with Poisson kernels, in smooth domains, and with rapidly oscillating data. The latter, in its own turn, might give accurate information about the boundary layer phenomena for numerical approximations and fast convergence of homogenization problems that has been much in focus lately.
(This is a joint work with Kiahm Lee.)