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

DOI10.1090/S0033-569X-07-01067-3zbMath1143.35314OpenAlexW2060175751MaRDI QIDQ3499461

P. A. Krutitskii

Publication date: 29 May 2008

Published in: Quarterly of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: http://www.ams.org/distribution/qam/2008-66-01/S0033-569X-07-01067-3/home.html

zbMATH Keywords

Dirichlet problemweak solutionclassical solutionLaplacianslits

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Integral representations of solutions to PDEs (35C15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (3)

The Dirichlet problem for the Laplacian with discontinuous boundary data in a 2D multiply connected exterior domain ⋮ Dirichlet problem for the Laplace equation in the exterior of open Lipschitz surfaces ⋮ On existence of a classical solution and nonexistence of a weak solution to the Dirichlet problem for the Laplacian with discontinuous boundary data

Cites Work

• The mixed harmonic problem in an exterior cracked domain with Dirichlet condition on cracks
• The 2-dimensional Dirichlet problem in an external domain with cuts
• Elliptic Partial Differential Equations of Second Order
• The Dirichlet problem for the two-dimensional Laplace equation in a multiply connected domain with cuts
• The integral representation for a solution of the 2‐d Dirichlet problem with boundary data on closed and open curves
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