Symmetries in an overdetermined problem for the Green's function

Details Symmetries in an overdetermined problem for the Green's function Symmetries in an overdetermined problem for the Green's function

2009-12-10

arxiv.org/abs/0912.1935v1

Mathematics

Analysis of PDEs

10 pages

Scientific paper

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.

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