Czechoslovak Mathematical Journal, Vol. 48, No. 4, pp. 763-784, 1998

Solution of the Neumann problem
for the Laplace equation

Dagmar Medkova

Zitna 25, 115 67 Praha 1, Czech Republic (Matematicky ustav AV CR)

Abstract: 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.

Keywords: single layer potential, generalized normal derivative

Classification (MSC 1991): 31B10, 35J05, 35J25

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