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Displaying similar documents to “Reflection and the Neumann problem on doubly connected regions”

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.