On an elaboration of M. Kac's theorem concerning eigenvalues of the Laplacian in a region with randomly distributed small obstacles

DOI10.1007/BF01206016zbMath0541.35019MaRDI QIDQ794198

Shin Ozawa

Publication date: 1983

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

random mediaLaplacianDirichlet conditionKac theoremrandomly distributed small obstaclessingular variation of domains

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

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Cites Work

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• On an elaboration of M. Kac's theorem concerning eigenvalues of the Laplacian in a region with randomly distributed small obstacles
• Point interaction potential approximation for \((-\Delta +U)^{-1}\) and eigenvalues of the Laplacian on wildly perturbed domain
• Singular variation of domains and eigenvalues of the Laplacian
• Potential and scattering theory on wildly perturbed domains
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