The spectrum asymptotics for the Dirichlet problem in the case of the biharmonic operator in a domain with highly indented boundary

DOI10.1090/S1061-0022-2011-01178-1zbMath1232.31001OpenAlexW1968202227MaRDI QIDQ3104492

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Publication date: 14 December 2011

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s1061-0022-2011-01178-1

zbMATH Keywords

Dirichlet problembiharmonic operatorrapid oscillationasymptotic expansions of eigenvalueseigenoscillations of the Kirchhoff platenonregular perturbation of the boundary

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30) Boundary value and inverse problems for harmonic functions in two dimensions (31A25)

Related Items (6)

Domain dependence of eigenvalues of elliptic type operators ⋮ On the asymptotic formulas for perturbations in the eigenvalues of the Stokes equations due to the presence of small deformable inclusions ⋮ Asymptotic expansion for solution of Maxwell equation in domain with highly oscillating boundary ⋮ Uniform resolvent convergence for strip with fast oscillating boundary ⋮ Hadamard asymptotics for eigenvalues of the Dirichlet Laplacian ⋮ On differentiability of eigenvalues of second order elliptic operators on non-smooth domains

Cites Work

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• Eigenoscillations of an elastic body with a rough surface
• Edge effect in the bending of a thin three-dimensional plate
• Roughness-induced effects on the quasi-geostrophic model
• On the Hadamard formula for nonsmooth domains
• Asymptotics of the solution of a Dirichlet problem in an angular domain with a periodically changing boundary
• Elliptic problems in domains with piecewise smooth boundaries
• Constructing wall laws with domain decomposition or asymptotic expansion techniques
• The inhomogeneous Dirichlet problem for \(\Delta^2\) in Lipschitz domains
• On three-dimensional effects near the vertex of a crack in a thin plate
• Asymptotics of solutions to the Poisson problem in a perforated domain with corners
• Rayleigh's conjecture on the principal frequency of the clamped plate
• On Rayleigh's conjecture for the clamped plate and its generalization to three dimensions
• Variational methods in shape optimization problems
• \(L^{q}\)-perturbations of leading coefficients of elliptic operators: Asymptotics of eigenvalues
• Convergence of convex sets and of solutions of variational inequalities
• JUNCTION IN A THIN MULTIDOMAIN FOR A FOURTH ORDER PROBLEM
• The Plate Paradox for Hard and Soft Simple Support
• Asymptotics of solutions and modelling the problems of elasticity theory in domains with rapidly oscillating boundaries
• Boundary Homogenization and Reduction of Dimension in a Kirchhoff–Love Plate
• Homogenization of a mixed boundary-value problem in a domain with anisotropic fractal perforation
• ASYMPTOTICS OF THE SOLUTION OF THE DIRICHLET PROBLEM FOR AN EQUATION WITH RAPIDLY OSCILLATING COEFFICIENTS IN A RECTANGLE
• [Russian Text Ignored.]
• [Russian Text Ignored]
• Rough boundaries and wall laws
• The polynomial property of self-adjoint elliptic boundary-value problems and an algebraic description of their attributes
• Stability of the domain related to the main problems of the theory of partial differential equations, especially in connection with the elasticity theory, I
• Effective laws for the Poisson equation on domains with curved oscillating boundaries
• Properties of solutions of ordinary differential equations in banach space
• On the roughness-induced effective boundary conditions for an incompressible viscous flow
• Boundary layers and boundary hinge-support conditions for thin plates

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