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. 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.
Original language | English |
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Pages (from-to) | 1-44 |
Number of pages | 44 |
Journal | Communications on Pure and Applied Mathematics |
Volume | 64 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2011 |
ASJC Scopus subject areas
- Mathematics (all)
- Applied Mathematics