Displaying similar documents to “On the convergence of Neumann series for noncompact operators”

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.

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...