Exact solutions to some external mixed problems in potential theory. (English) Zbl 0625.31004

This paper deals with exact solutions of mixed problems in a half-space. Two problems are discussed: (1) Find a harmonic function W in a half- space \(z\geq 0\) satisfying, on the plane \(z=0\), \(W=w\) outside a circle and \(\partial W/\partial z=0\) inside the circle, where w is a given function outside the circle, (2) Find a harmonic function W in the half-space satisfying \(\partial W/\partial z=\sigma\) outside a circle and \(W=0\) inside the circle, where \(\sigma\) is a given function outside the circle. Integral representations of the solutions and several examples are given.
Reviewer: M.Sakai


31B10 Integral representations, integral operators, integral equations methods in higher dimensions
31B20 Boundary value and inverse problems for harmonic functions in higher dimensions
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