We consider Serrin's overdetermined problem for the equation v+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 / G. Ciraolo, L. Vezzoni. - In: MANUSCRIPTA MATHEMATICA. - ISSN 0025-2611. - 159:3-4(2019), pp. 445-452. [10.1007/s00229-018-1079-z]
On Serrin’s overdetermined problem in space forms
G. Ciraolo;
2019
Abstract
We consider Serrin's overdetermined problem for the equation v+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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