The Neumann problem for the 2-D Helmholtz equation in a domain, bounded by closed and open curves.
Krutitskii, P.A. (1998)
International Journal of Mathematics and Mathematical Sciences
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Displaying similar documents to “A problem related to the Hall effect in a semiconductor with an electrode of an arbitrary shape.”
The Neumann problem for the 2-D Helmholtz equation in a domain, bounded by closed and open curves.
Method of interior boundaries in a mixed problem of acoustic scattering.
Krutitskii, P.A. (1999)
Mathematical Problems in Engineering
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Explicit solution of the jump problem for the Laplace equation and singularities at the edges.
Krutitskii, P.A. (2001)
Mathematical Problems in Engineering
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The boundary-value problems for Laplace equation and domains with nonsmooth boundary
Dagmar Medková (1998)
Archivum Mathematicum
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Dirichlet, Neumann and Robin problem for the Laplace equation is investigated on the open set with holes and nonsmooth boundary. The solutions are looked for in the form of a double layer potential and a single layer potential. The measure, the potential of which is a solution of the boundary-value problem, is constructed.
Boundary integral equations of elasticity in domains with piecewise smooth boundaries
Maz'ya, Vladimir G.
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Two-dimensional boundary value problems of statics of the theory of elastic mixtures.
Basheleishvili, Michael (1995)
Memoirs on Differential Equations and Mathematical Physics
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Solution of the Neumann problem for the Laplace equation
Dagmar Medková (1998)
Czechoslovak Mathematical Journal
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For fairly general open sets it is shown that we can express a solution of the Neumann problem for the Laplace equation in the form of a single layer potential of a signed measure which is given by a concrete series. If the open set is simply connected and bounded then the solution of the Dirichlet problem is the double layer potential with a density given by a similar series.