6533b7dafe1ef96bd126d884
RESEARCH PRODUCT
On Serrin’s overdetermined problem in space forms
Giulio CiraoloLuigi Vezzonisubject
Pure mathematicsGeneral Mathematics010102 general mathematicsMathematical analysisAlgebraic geometrySpace (mathematics)Curvature01 natural sciencesDelta-v (physics)Overdetermined systemNumber theorySettore MAT/05 - Analisi Matematica0103 physical sciencesEuclidean geometryMathematics (all)010307 mathematical physics0101 mathematicsSymmetry (geometry)Mathematicsdescription
We consider Serrin’s overdetermined problem for the equation $$\Delta v + nK v = -\,1$$ 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-10-19 |