arXiv:0912.1935 Abstract | arXiv Analytics

arXiv:0912.1935 [math.AP]Abstract References Reviews Resources

Symmetries in an overdetermined problem for the Green's function

Published 2009-12-10Version 1

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.

Comments: 10 pages

Categories: math.AP

Subjects: 35N25, 35J08, 35B06

Keywords: greens function, overdetermined problem, conformal mappings, normal derivative, symmetry results

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