Symmetries in an overdetermined problem for the Green's function
Virginia Agostiniani - SISSA, via Bonomea 265, 34136 Trieste, Italy (email)
Abstract: 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.
Keywords: Overdetermined boundary values problems, Green's function, symmetries.
Received: September 2009; Revised: January 2010; Available Online: November 2010.
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