Displaying similar documents to “Generalized Robin problem in potential theory”

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.

The third boundary value problem in potential theory for domains with a piecewise smooth boundary

Dagmar Medková (1997)

Czechoslovak Mathematical Journal

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The paper investigates the third boundary value problem ∂ u ∂ n + λ u = μ for the Laplace equation by the means of the potential theory. The solution is sought in the form of the Newtonian potential (1), (2), where ν is the unknown signed measure on the boundary. The boundary condition (4) is weakly characterized by a signed measure T ν . Denote by T ν → T ν the corresponding operator on the space of signed measures on the boundary of the investigated domain G . If there is α ≠ 0 such that the essential spectral radius...

Solution of the Robin problem for the Laplace equation

Dagmar Medková (1998)

Applications of Mathematics

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For open sets with a piecewise smooth boundary it is shown that we can express a solution of the Robin problem for the Laplace equation in the form of a single layer potential of a signed measure which is given by a concrete series.