The boundary-value problems for Laplace equation and domains with nonsmooth boundary

Dagmar Medková

Displaying similar documents to “The boundary-value problems for Laplace equation and domains with nonsmooth boundary”

Continuous extendibility of solutions of the Neumann problem for the Laplace equation

Dagmar Medková (2003)

Czechoslovak Mathematical Journal

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A necessary and sufficient condition for the continuous extendibility of a solution of the Neumann problem for the Laplace equation is given.

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.

Solution of the Dirichlet problem for the Laplace equation

Dagmar Medková (1999)

Applications of Mathematics

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For open sets with a piecewise smooth boundary it is shown that a solution of the Dirichlet problem for the Laplace equation can be expressed in the form of the sum of the single layer potential and the double layer potential with the same density, where this density is given by a concrete series.