The Dirichlet problem for the equation \(\Delta u - k^2u = 0\) in the exterior of nonclosed Lipschitz surfaces

DOI10.1155/2013/302628zbMath1268.35035OpenAlexW2071464226WikidataQ58988662 ScholiaQ58988662MaRDI QIDQ1950011

P. A. Krutitskii

Publication date: 23 May 2013

Published in: International Journal of Mathematics and Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2013/302628

zbMATH Keywords

Dirichlet problemweak solutionexistenceuniquenessLaplace equationexterior of nonclosed Lipschitz surfacesintegral representation for a solution

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Integral representations of solutions to PDEs (35C15) Weak solutions to PDEs (35D30)

Cites Work

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• The 2D Dirichlet problem for the propagative Helmholtz equation in an exterior domain with cracks and singularities at the edges
• Problem of diffraction at a fine screen
• Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
• The 2-dimensional Dirichlet problem in an external domain with cuts
• The Dirichlet problem for the 2D-Laplace equation in a domain with cracks without compatibility conditions at tips of the cracks
• The \(L^p\)-solvability of the Dirichlet problem for planar elliptic equations, sharp results
• Covariant field theory on frame bundles of fibered manifolds
• On the Poisson integral for Lipschitz and $C^{1}$-domains
• The Neumann problem on Lipschitz domains
• The Dirichlet Problem for the 2‐D Helmholtz Equation in a Multiply Connected Domain with Cuts
• The Dirichlet problem for the two-dimensional Laplace equation in a multiply connected domain with cuts

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