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

Regularity of boundary data in periodic homogenization of elliptic systems in layered media 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 Gérard-Varet and Masmoudi (Acta Math. 209:133–178, 2012), and by Prange (SIAM J. Math. Anal. 45(1):345–387, 2012), 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. Manuscripta Mathematica Springer Journals

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

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Springer Berlin Heidelberg
Copyright © 2016 by Springer-Verlag Berlin Heidelberg
Mathematics; Mathematics, general; Algebraic Geometry; Topological Groups, Lie Groups; Geometry; Number Theory; Calculus of Variations and Optimal Control; Optimization
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