Agostiniani, Virginia; Magnanini, Rolando Symmetries in an overdetermined problem for the Green’s function. (English) Zbl 1210.35169 Discrete Contin. Dyn. Syst., Ser. S 4, No. 4, 791-800 (2011). Summary: 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. Cited in 13 Documents MSC: 35N25 Overdetermined boundary value problems for PDEs and systems of PDEs 35J08 Green’s functions for elliptic equations 35B06 Symmetries, invariants, etc. in context of PDEs Keywords:overdetermined boundary values problems; Green’s function; symmetries PDFBibTeX XMLCite \textit{V. Agostiniani} and \textit{R. Magnanini}, Discrete Contin. Dyn. Syst., Ser. S 4, No. 4, 791--800 (2011; Zbl 1210.35169) Full Text: DOI arXiv