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.

On Serrin’s overdetermined problem in space forms

Ciraolo G.;Vezzoni L.
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
159
3-4
445
452
http://link.springer-ny.com/link/service/journals/00229/index.htm
Ciraolo G.; Vezzoni L.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1728645
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