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.
|Titolo:||Symmetries in an overdetermined problem for the Green's function|
|Data di pubblicazione:||2011|
|Appare nelle tipologie:||01.01 Articolo in Rivista|