The Dirichlet problem for the two-dimensional Laplace equation in a multiply connected domain with cuts

DOI10.1017/S0013091500020952zbMath0942.31002OpenAlexW2068059250MaRDI QIDQ4488184

P. A. Krutitskii

Publication date: 9 July 2000

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0013091500020952

zbMATH Keywords

Dirichlet problemLaplace equationcracked domain

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Boundary value problems in the complex plane (30E25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Integral representations, integral operators, integral equations methods in two dimensions (31A10) Integral equations with kernels of Cauchy type (45E05) Boundary value and inverse problems for harmonic functions in two dimensions (31A25)

Related Items (15)

On the harmonic Dirichlet problem on a two-dimensional domain with cuts ⋮ Quadrature formula for the direct value of the double-layer potential ⋮ The Dirichlet problem for the 2D-Laplace equation in a domain with cracks without compatibility conditions at tips of the cracks ⋮ On existence of a classical solution and non-existence of a weak solution to the Dirichlet problem in a planar domain with slits for Laplacian ⋮ On the properties of solutions of the harmonic Dirichlet problem in a two-dimensional domain with cuts ⋮ Laplace equation and Poisson integral ⋮ The Dirichlet problem for the equation \(\Delta u - k^2u = 0\) in the exterior of nonclosed Lipschitz surfaces ⋮ On the modified jump problem for the Laplace equation in the exterior of cracks in a plane ⋮ The mixed harmonic problem in a bounded cracked domain with Dirichlet condition on cracks. ⋮ The third problem for the Laplace equation on a planar cracked domain with modified jump conditions on cracks ⋮ Dirichlet problem for the Laplace equation in the exterior of open Lipschitz surfaces ⋮ The modified jump problem for the Laplace equation and singularities at the tips ⋮ Quadrature formula for the harmonic double layer potential ⋮ On existence of a classical solution and nonexistence of a weak solution to the Dirichlet problem for the Laplacian with discontinuous boundary data ⋮ High-order Galerkin method for Helmholtz and Laplace problems on multiple open arcs

Cites Work

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• The Neumann problem for the 2-D Helmholtz equation in a multiply connected domain with cuts
• THE ANGULAR POTENTIAL AND SOME OF ITS APPLICATIONS
• Fast stratified flow over several obstacles, including wings
• The Dirichlet Problem for the 2‐D Helmholtz Equation in a Multiply Connected Domain with Cuts
• Wave propagation in a 2-D external domain with cuts

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