Regularity of boundary data in periodic homogenization of elliptic systems in layered media

Abstract

In this note we study periodic homogenization of Dirichlet problem for divergence type elliptic systems when both the coefficients and the boundary data are oscillating. One of the key difficulties here is the determination of the fixed boundary data corresponding to the limiting (homogenized) problem. This issue has been addressed in recent papers by D. Gérard-Varet and N. Masmoudi, and by C. Prange, however, not much is known about the regularity of this fixed data. The main objective of this note is to initiate a study of this problem, and to prove several regularity results in this connection.

Final revision addressing referee remarks

References in corpus (4)

• The Green function estimates for strongly elliptic systems of second order
• Green's matrices of second order elliptic systems with measurable coefficients in two dimensional domains
• Applications of Fourier analysis in homogenization of Dirichlet problem III: Polygonal Domains
• Slow convergence in periodic homogenization problems for divergence type elliptic operators

Cited by in corpus (1)

• Continuity Properties for Divergence Form Boundary Data Homogenization Problems