Behavior of solutions of the Poisson equation under fragmentation of the boundary of the domain

DOI10.1007/BF03167892zbMath0702.35012MaRDI QIDQ3480439

Satoshi Kaizu

Publication date: 1990

Published in: Japan Journal of Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

holesRobin boundary conditionsemilinear boundary conditionsfragmented boundaries

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) 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)

Related Items (2)

Homogenization of the heat equation for a domain with a network of pipes with a well-mixed fluid ⋮ Operator estimates for homogenization of the Robin Laplacian in a perforated domain

Cites Work

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• Point interaction potential approximation for \((-\Delta +U)^{-1}\) and eigenvalues of the Laplacian on wildly perturbed domain
• A monotone boundary condition for a domain with many tiny spherical holds
• The Robin problems on domains with many tiny holes
• An average effect of many tiny holes in nonlinear boundary value problems with monotone boundary conditions
• Homogenization of eigenvalue problems in perforated domains
• Potential and scattering theory on wildly perturbed domains
• Probabilistic methods in some problems of scattering theory
• THE ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF THE SECOND BOUNDARY VALUE PROBLEM UNDER FRAGMENTATION OF THE BOUNDARY OF THE DOMAIN
• THE FIRST BOUNDARY VALUE PROBLEM IN DOMAINS WITH A COMPLICATED BOUNDARY FOR HIGHER ORDER EQUATIONS
• THE METHOD OF ORTHOGONAL PROJECTIONS AND THE DIRICHLET PROBLEM IN DOMAINS WITH A FINE-GRAINED BOUNDARY

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