The Neumann problem for the 2-D Helmholtz equation in a multiply connected domain with cuts

DOI10.4171/ZAA/766zbMath0882.73019OpenAlexW2024436681MaRDI QIDQ1363048

P. A. Krutitskii

Publication date: 22 February 1998

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/zaa/766

zbMATH Keywords

potential theorycracksscreensFredholm equation of second kindexistence of classical solution

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Bulk waves in solid mechanics (74J10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boundary value and inverse problems for harmonic functions in two dimensions (31A25)

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The integral representation for a solution of the 2‐d Dirichlet problem with boundary data on closed and open curves ⋮ Scattering of tidal waves by reefs and spits ⋮ Quadrature formula for a double layer potential in the case of the Helmholtz equation ⋮ Quadrature formula for the direct value of the double-layer potential ⋮ Neumann problem for the Helmholtz equation in the exterior of nonclosed surfaces and the case of its explicit solution ⋮ Mixed boundary value problems of diffraction by a half‐plane with an obstacle perpendicular to the boundary ⋮ The jump problem for the Laplace equation ⋮ The Neumann problem in a 2-D exterior domain with cuts and singularities at the tips ⋮ The Dirichlet problem for the two-dimensional Laplace equation in a multiply connected domain with cuts ⋮ The jump problem for the Helmholtz equation and singularities at the edges ⋮ The Neumann problem for the dissipative Helmholtz equation in the exterior of open Lipschitz surfaces

Cites Work

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• Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
• Three-dimensional Dirichlet problem for the Helmholtz equation for an open boundary
• Potential techniques for boundary value problems on \(C^1\)-domains
• Dirichlet's problem for the Helmholtz equation outside cuts in a plane
• Neumann's problem for the Helmholtz equation outside cuts in the plane
• The Dirichlet problem for the two-dimensional Helmholtz equation for an open boundary
• Layer potentials and boundary value problems for the helmholtz equation in the complement of a thin obstacle
• Boundary integral equations for mixed Dirichlet, Neumann and transmission problems
• The Neumann problem on Lipschitz domains
• A space-time variational formulation for the boundary integral equation in a 2D elastic crack problem
• On the transient acoustic scattering by a flat object

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