Layer Potential Methods for Elliptic Homogenization Problems

2009/10/21 by Carlos Kenig, Kenig, Carlos, Zhongwei Shen +1 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.0910.4169

arxiv created 2009/10/21 · arxiv updated 2009/12/01

Abstract

In this paper we use the method of layer potentials to study L² boundary value problems in a bounded Lipschitz domain Ω for a family of second order elliptic systems with rapidly oscillating periodic coefficients, arising in the theory of homogenization. Let L_ε=-div(A(ε^-1X)∇ ). Under the assumption that A(X) is elliptic, symmetric, periodic and Hölder continuous, we establish the solvability of the L² Dirichlet, regularity, and Neumann problems for L_ε (u_ε)=0 in Ω with optimal estimates uniform in ε>0.

Cited by

• Periodic homogenization and harmonic measures

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• The Methods of Layer Potentials for General Elliptic Homogenization Problems in Lipschitz Domains
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