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Symmetries in an overdetermined problem for the Green's function

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  • We consider in the plane the problem of reconstructing a domain from the normal derivative of its Green's function with pole at a fixed point in the domain. By means of the theory of conformal mappings, we obtain existence, uniqueness, (non-spherical) symmetry results, and a formula relating the curvature of the boundary of the domain to the normal derivative of its Green's function.
    Mathematics Subject Classification: Primary: 35N25; Secondary: 35J08, 35B06.


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