Layer potential methods for elliptic homogenization problems

DOI10.1002/cpa.20343zbMath1213.35063arXiv0910.4169OpenAlexW2045295430WikidataQ125776210 ScholiaQ125776210MaRDI QIDQ3068370

Carlos E. Kenig, Zhongwei Shen

Publication date: 14 January 2011

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.4169

zbMATH Keywords

double-layer potentialssingular operatorsingle-layer potentialRellich property

Mathematics Subject Classification ID

Integral representations of solutions to PDEs (35C15) Homogenization in equilibrium problems of solid mechanics (74Q05) Boundary behavior of harmonic functions in higher dimensions (31B25) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Boundary value problems for second-order elliptic systems (35J57)

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Cites Work

• Unnamed Item
• Layer potentials and boundary value problems for elliptic systems in Lipschitz domains
• Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
• Homogenization of elliptic problems with \(L^p\) boundary data
• Boundary layer methods for Lipschitz domains in Riemannian manifolds
• The Neumann problem for elliptic equations with non-smooth coefficients
• Homogenization of Poisson's kernel and applications to boundary control
• Necessary and sufficient conditions for the solvability of the \(L^p\) Dirichlet problem on Lipschitz domains
• The Green function estimates for strongly elliptic systems of second order
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• Compactness methods in the theory of homogenization
• Compactness methods in the theory of homogenization II: Equations in non-divergence form
• L^p bounds on singular integrals in homogenization
• Potential theory on Lipschitz domains in Riemannian manifolds: \(L^p\) Hardy, and Hölder space results

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