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.
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