The third boundary value problem in potential theory

Ivan Netuka

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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...