Discrete and Continuous Dynamical Systems - Series S (DCDS-S)

Symmetries in an overdetermined problem for the Green's function

Pages: 791 - 800, Volume 4, Issue 4, August 2011      doi:10.3934/dcdss.2011.4.791

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Virginia Agostiniani - SISSA, via Bonomea 265, 34136 Trieste, Italy (email)
Rolando Magnanini - Dipartimento di Matematica "U. Dini", Università degli Studi di Firenze, viale Morgagni 67/A, 50134 Firenze, 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.
Mathematics Subject Classification:  Primary: 35N25; Secondary: 35J08, 35B06.

Received: September 2009;      Revised: January 2010;      Available Online: November 2010.