perturbation

Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains

  • Boundary Value Problems for the Laplace Operator in Domains Perturbed Near Isolated Singularities
    • Dirichlet and Neumann Problems for the Laplace Operator in Domains with Corners and Cone Vertices
      • Boundary Value Problems for the Laplace Operator in a Strip
        • The Dirichlet problem
        • The complex Fourier transform
        • Asymptotics of solution of the Dirichlet problem
      • Boundary Value Problems for the Laplace Operator in a Sector
      • The Dirichlet Problem in a Bounded Domain with Corner
        • Solvability of the boundary value problem
        • Particular solutions of the homogeneous problem
      • The Neumann Problem in a Bounded Domain with a Corner
    • Dirichlet and Neumann Problems in Domains with Singularly Perturbed Boundaries
      • Boundary Value Problems for the Laplace Operator in a Strip
    • Elliptic Boundary Value Problems in Domains with Smooth Boundaries, in a Cylinder, and in Domains with Cone Vertices
    • Asymptotics of Solutions to General Elliptic Boundary Value Problems in Domains Perturbed Near Cone Vertices
    • Variants and Corollaries of the Asymptotic Theory
    • Boundary Value Problems for the Laplace Operator in a Punctured Domain and the Exterior of a Bounded Planar Domain
  • Asymptotic Behaviour of Functionals on Solutions of Boundary Value Problems in Domains Perturbed Near Isolated Boundary Singularities
    • Asymptotic Behaviour of Intensity Factors for Vertices of Corners and Cones Coming Close
    • Asymptotic Behaviour of Energy Integrals for Small Perturbations of the Boundary Near Corners and Isolated Points
    • Asymptotic Behaviour of Energy Integrals for Particular Problems of Mathematical Physics
  • Asymptotic Behaviour of Eigenvalues of Boundary Value Problems in Domains with Small Holes
    • Asymptotic Behaviour of the First Eigenvalue of a Mixed Boundary Value Problem
    • Asymptotic Expansions of Eigenvalues of Other Boundary Value Problems
  • Homogeneous Solutions of Boundary Value Problems in the Exterior of a Thin Cone
    • Formal Asymptotic Representation