TY - JOUR
T1 - Layer potential methods for elliptic homogenization problems
AU - Kenig, Carlos E.
AU - Shen, Zhongwei
PY - 2011/1
Y1 - 2011/1
N2 - 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. Defining, 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 in Ω with optimal estimates uniform in ε>0.
AB - 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. Defining, 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 in Ω with optimal estimates uniform in ε>0.
UR - http://www.scopus.com/inward/record.url?scp=78049357724&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=78049357724&partnerID=8YFLogxK
U2 - 10.1002/cpa.20343
DO - 10.1002/cpa.20343
M3 - Article
AN - SCOPUS:78049357724
SN - 0010-3640
VL - 64
SP - 1
EP - 44
JO - Communications on Pure and Applied Mathematics
JF - Communications on Pure and Applied Mathematics
IS - 1
ER -