Layer potential methods for elliptic homogenization problems

Carlos E. Kenig; Zhongwei Shen

doi:10.1002/cpa.20343

Layer potential methods for elliptic homogenization problems

Carlos E. Kenig
, Zhongwei Shen

Research output: Contribution to journal › Article › peer-review

54 Scopus citations

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
Pages (from-to)	1-44
Number of pages	44
Journal	Communications on Pure and Applied Mathematics
Volume	64
Issue number	1
DOIs	https://doi.org/10.1002/cpa.20343
State	Published - Jan 2011

Funding

Funders	Funder number
Directorate for Mathematical and Physical Sciences	0456583, 0855294

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1002/cpa.20343

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title = "Layer potential methods for elliptic homogenization problems",

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 H{\"o}lder-continuous, we establish the solvability of the L2 Dirichlet, regularity, and Neumann problems for in Ω with optimal estimates uniform in ε>0.",

author = "Kenig, \{Carlos E.\} and Zhongwei Shen",

year = "2011",

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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 - https://www.scopus.com/pages/publications/78049357724

UR - https://www.scopus.com/pages/publications/78049357724#tab=citedBy

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 -

Layer potential methods for elliptic homogenization problems

Abstract

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