On boundary value problem with singular inhomogeneity concentrated on the boundary

DOI10.1016/j.matpur.2011.11.002zbMath1277.35142OpenAlexW2058681007MaRDI QIDQ441891

Gregory A. Chechkin, Doina Cioranescu, Alain Damlamian, Andrey L. Piatnitski

Publication date: 8 August 2012

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2011.11.002

zbMATH Keywords

homogenizationmass concentrationperiodic unfoldingstrange term

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (9)

Weakly singular Steklov condition in the multidimensional case ⋮ PDE problems with concentrating terms near the boundary ⋮ Existence of solutions for fractional differential inclusions with separated boundary conditions in Banach space ⋮ A model of a boundary composed of the Helmholtz resonators ⋮ Spectral properties of an elliptic operator with double-contrast coefficients near a hyperplane ⋮ On the behavior of the spectrum of a perturbed Steklov boundary value problem with a weak singularity ⋮ Estimate of the spectrum deviation of the singularly perturbed Steklov problem ⋮ Neumann spectral problem in a domain with very corrugated boundary ⋮ Homogenization of a quasilinear elliptic problem in domains with small holes

Cites Work

• On the vibration of a partially fastened membrane with many `light' concentrated masses on the boundary
• Boundary homogenization for elliptic problems
• Asymptotic expansions of local eigenvibrations for plate with density perturbed in neighborhood of one-dimensional manifold
• Estimation of solutions of boundary-value problems in domains with concentrated masses located periodically along the boundary: case of light masses
• On the precise asymptotics of the constant in Friedrich's inequality for functions vanishing on the part of the boundary with microinhomogeneous structure
• The periodic unfolding method for perforated domains and Neumann sieve models
• Asymptotic expansions of eigenvalues and eigenfunctions of an elliptic operator in a domain with many “light” concentrated masses situated on the boundary. Two-dimensional case
• Asymptotic behaviour of an elastic body with a surface having small stuck regions
• Perturbation of the eigenvalues of a membrane with a concentrated mass
• AVERAGING OF BOUNDARY VALUE PROBLEMS WITH A SINGULAR PERTURBATION OF THE BOUNDARY CONDITIONS
• Non-periodic boundary homogenization and "light" concentrated masses
• VIBRATIONS OF A THICK PERIODIC JUNCTION WITH CONCENTRATED MASSES
• Complete WKB asymptotics of high frequency vibrations in a stiff problem
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