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
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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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