Dirichlet problems on varying domains.

DOI10.1016/S0022-0396(02)00105-5zbMath1090.35069MaRDI QIDQ1869777

Daniel Daners

Publication date: 28 April 2003

Published in: Journal of Differential Equations (Search for Journal in Brave)

zbMATH Keywords

convergencedomainBoundary value problems for second-order elliptic equationssingular perturbation of domain

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25)

Related Items (48)

Local and global uniform convergence for elliptic problems on varying domains ⋮ Capacity and Faber-Krahn inequality in \(\mathbb R^{n}\) ⋮ Neumann Laplacian in a perturbed domain ⋮ Spectral theory for perturbed Krein Laplacians in nonsmooth domains ⋮ Spectral stability of general non-negative selfadjoint operators with applications to Neumann-type operators ⋮ Unique continuation from the edge of a crack ⋮ Convergence of Dirichlet eigenvalues for elliptic systems on perturbed domains ⋮ Uniform stability of the Dirichlet spectrum for rough outer perturbations ⋮ Finite-Element Domain Approximation for Maxwell Variational Problems on Curved Domains ⋮ Spectral convergence of the Laplace operator with Robin boundary conditions on a small hole ⋮ Effects of small boundary perturbation on flow of viscous fluid ⋮ The \(C^{r}\) dependence problem of eigenvalues of the Laplace operator on domains in the plane ⋮ Computing eigenvalues of the Laplacian on rough domains ⋮ Spectral stability under removal of small capacity sets and applications to Aharonov-Bohm operators ⋮ Behaviour of the Stokes operators under domain perturbation ⋮ Magnetic Neumann Laplacian on a domain with a hole ⋮ Persistence of bounded solutions of parabolic equations under domain perturbation ⋮ Singularity of eigenfunctions at the junction of shrinking tubes. I ⋮ Perturbed eigenvalues of polyharmonic operators in domains with small holes ⋮ The nodal line of the second eigenfunction of the Robin Laplacian in \(\mathbb R^2\) can be closed ⋮ Singularity of eigenfunctions at the junction of shrinking tubes. Part II ⋮ On the sharp effect of attaching a thin handle on the spectral rate of convergence ⋮ On the convergence of solutions for SPDEs under perturbation of the domain ⋮ Eigenvalues of the Laplacian with moving mixed boundary conditions: the case of disappearing Dirichlet region ⋮ Domain variation and non-uniqueness of homoclinic solutions of some partial differential equations on strips ⋮ Weak and strong approximation of semigroups on Hilbert spaces ⋮ Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations ⋮ Waveguides with combined Dirichlet and Robin boundary conditions ⋮ Sharp convergence rate of eigenvalues in a domain with a shrinking tube ⋮ Layer potential techniques in spectral analysis. Part I: Complete asymptotic expansions for eigenvalues of the Laplacian in domains with small inclusions ⋮ Domain perturbation and invariant manifolds ⋮ A Survey on the Krein–von Neumann Extension, the Corresponding Abstract Buckling Problem, and Weyl-type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains ⋮ The Hardy inequality and the heat equation in twisted tubes ⋮ Perturbation of semi-linear evolution equations under weak assumptions at initial time ⋮ A Faber-Krahn inequality for Robin problems in any space dimension ⋮ Boundary element methods for acoustic scattering by fractal screens ⋮ On the Placement of an Obstacle So As to Optimize the Dirichlet Heat Trace ⋮ Weak convergence, local bifurcations and uniqueness theorems ⋮ Wildly perturbed manifolds: norm resolvent and spectral convergence ⋮ Effective Fluid Behavior in Domain with Rough Boundary and the Darcy--Weisbach Law ⋮ Two-dimensional Helmholtz equation with zero Dirichlet boundary condition on a circle: Analytic results for boundary deformation, the transition disk-lens ⋮ Exhaustion approximation for the control problem of the heat or Schrödinger semigroup on unbounded domains ⋮ DOMAIN PERTURBATION FOR PARABOLIC EQUATIONS ⋮ Generalizations and Properties of the Principal Eigenvalue of Elliptic Operators in Unbounded Domains ⋮ Geometrically induced phase transitions in two-dimensional dumbbell-shaped domains ⋮ On differentiability of eigenvalues of second order elliptic operators on non-smooth domains ⋮ A fractional Dirichlet-to-Neumann operator on bounded Lipschitz domains ⋮ Eigenvalues of the Laplacian with moving mixed boundary conditions: the case of disappearing Neumann region

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