# Analysis Seminar

#### Boundary Layers in Periodic Homogenization of Neumann Problems

Speaker: Zhongwei Shen, University of Kentucky

Location: Warren Weaver Hall 1302

Date: Thursday, March 2, 2017, 11 a.m.

Synopsis:

This talk is concerned with a family of second-order elliptic systems in divergence form with rapidly oscillating periodic coefficients. We initiate the study of homogenization and boundary layers for Neumann problems with first-order oscillating boundary data. The investigation is motivated by the study of higher-order convergence rates for Neumann problems with non-oscillating data. We identify the homogenized system and establish the sharp rate of convergence in $$L^2$$. Sharp regularity estimates are also obtained for the homogenized boundary data in both Dirichlet and Neumann problems. Our results as well as the approaches used build on the work of D. Gerard-Varet - N. Masmoudi and S.N. Armstrong - T. Kuusi - J.C. Mourrat - C. Prange for the Dirichlet problem. This is a joint work with Jinping Zhuge.