We consider Serrin’s overdetermined problem for the equation Δv+nKv=-1 in space forms, where K is the curvature of the space, and we prove a symmetry result by using a P-function approach. Our approach generalizes the one introduced by Weinberger to space forms and, as in the Euclidean case, it provides a short proof of the symmetry result which does not make use of the method of moving planes.

Ciraolo, G., Vezzoni, L. (2019). On Serrin’s overdetermined problem in space forms. MANUSCRIPTA MATHEMATICA, 159(3-4), 445-452 [10.1007/s00229-018-1079-z].

On Serrin’s overdetermined problem in space forms

Ciraolo, Giulio
;
2019-01-01

Abstract

We consider Serrin’s overdetermined problem for the equation Δv+nKv=-1 in space forms, where K is the curvature of the space, and we prove a symmetry result by using a P-function approach. Our approach generalizes the one introduced by Weinberger to space forms and, as in the Euclidean case, it provides a short proof of the symmetry result which does not make use of the method of moving planes.
2019
Settore MAT/05 - Analisi Matematica
Ciraolo, G., Vezzoni, L. (2019). On Serrin’s overdetermined problem in space forms. MANUSCRIPTA MATHEMATICA, 159(3-4), 445-452 [10.1007/s00229-018-1079-z].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/316590
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