On existence of a classical solution and nonexistence of a weak solution to the Dirichlet problem for the Laplacian with discontinuous boundary data

DOI10.1090/S0033-569X-09-01130-1zbMath1170.35378OpenAlexW2072890910MaRDI QIDQ3632494

P. A. Krutitskii

Publication date: 11 June 2009

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

Full work available at URL: http://www.ams.org/distribution/qam/2009-67-02/S0033-569X-09-01130-1/home.html

zbMATH Keywords

Dirichlet problemLaplace equationdiscontinuous boundary data

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)

Cites Work

• The mixed harmonic problem in a bounded cracked domain with Dirichlet condition on 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
• Elliptic Partial Differential Equations of Second Order
• L'équation de Laplace avec conditions aux limites discontinues : convergence d'une discrétisation par éléments spectraux
• The Dirichlet problem for the two-dimensional Laplace equation in a multiply connected domain with cuts
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