On the convergence of Neumann series for noncompact operators

Dagmar Medková

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

On Neumann operators.

Teresa Bermúdez, Antonio Martinón (1992)

Extracta Mathematicae

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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 $\frac{\partial u}{\partial n} + λ u = μ$ 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 $T ν \to T ν$ the corresponding operator on the space of signed measures on the boundary of the investigated domain $G$ . If there is $α \neq 0$ such that the essential spectral radius...