On boundary-value problems for the Laplacian in bounded domains with micro inhomogeneous structure of the boundaries

DOI10.1007/s10114-005-0849-1zbMath1116.35010OpenAlexW2059248927MaRDI QIDQ884883

Gregory A. Chechkin, Rustem R. Gadyl'shin

Publication date: 7 June 2007

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-005-0849-1

zbMATH Keywords

variational formulationHomogenizationspectral problemshomogeneous Dirichlet boundary conditionsrapidly alternating boundary conditions

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (8)

Homogenization of a mixed boundary condition ⋮ Rate of convergence of eigenvalues to singularly perturbed Steklov-type problem for elasticity system ⋮ Rigorous justification of the effective boundary condition on a porous wall via homogenization ⋮ 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 ⋮ Newton’s Method for Convex Optimization ⋮ Boundary homogenization with large reaction terms on a strainer-type wall ⋮ Homogenization for Alternating Boundary Conditions with Large Reaction Terms Concentrated in Small Regions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On asymptotics of solutions and eigenvalues of the boundary value problem with rapidly alternating boundary conditions for the system of elasticity
• On a Laplacian with frequently nonperiodically alternating boundary conditions
• The boundary value problems of mathematical physics. Transl. from the Russian by Jack Lohwater
• Boundary homogenization for elliptic problems
• An introduction to \(\Gamma\)-convergence
• Homogenization and asymptotics for a membrane with closely spaced clamping points
• Asymptotic expansions and numerical algorithms of eigenvalues and eigenfunctions of the Dirichlet problem for second order elliptic equations in perforated domains
• On the spectrum of the Laplacian with frequently alternating boundary conditions
• Averaging operators with boundary conditions of fine-scaled structure
• Boundary value problem for the Laplacian with rapidly oscillating boundary conditions
• Perturbation theory for linear operators.
• Two-parameter asymptotics in a boundary value problem for the Laplacian.
• On the averaging of solutions of a second order elliptic equation with nonperiodic rapidly changing boundary conditions
• A boundary value problem for the~Laplacian with rapidly changing type of~boundary conditions in a~multidimensional domain
• Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes. I: Abstract framework, a volume distribution of holes
• Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes. II: Non-critical sizes of the holes for a volume distribution and a surface distribution of holes
• Linear and quasilinear elliptic equations
• On the Convergence of the Energy, Stress Tensors, and Eigenvalues in Homogenization Problems of Elasticity
• Asymptotic behaviour of an elastic body with a surface having small stuck regions
• AVERAGING OF BOUNDARY VALUE PROBLEMS WITH A SINGULAR PERTURBATION OF THE BOUNDARY CONDITIONS
• Effective permeability of the boundary of a domain
• Boundary-value problem in a cylinder with frequently changing type of boundary
• Effective Membrane Permeability: Estimates and Low Concentration Asymptotics
• On an analog of the Helmholtz resonator in the averaging theory
• Isoperimetric Inequalities in Mathematical Physics. (AM-27)

This page was built for publication: On boundary-value problems for the Laplacian in bounded domains with micro inhomogeneous structure of the boundaries