On Serrin’s overdetermined problem in space forms

By Giulio Ciraolo, Luigi Vezzoni. Manuscripta mathematica, 2017

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We consider Serrin’s overdetermined problem for the equation $$\Delta v + nK v = -\,1$$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.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/790af64a7c892f957897d7ef41ab9dd59290fea0