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.

Symmetries in an overdetermined problem for the Green's function / V. Agostiniani; R. Magnanini. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S. - ISSN 1937-1632. - STAMPA. - 4(2011), pp. 791-800. [10.3934/dcdss.2011.4.791]

Symmetries in an overdetermined problem for the Green's function

MAGNANINI, ROLANDO
2011

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.
4
791
800
V. Agostiniani; R. Magnanini
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2158/392578
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