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arXiv · 1901.05838

A symmetry property for elliptic equations on the sphere

Phillipo Lappicy
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Abstract

The goal of this paper is to study how the symmetry of the spherical domain influences solutions of elliptic equations on such domain. The method pursued is a variant of the moving plane method, discovered by Alexandrov (1962) and used for differential equations by Gidas, Ni and Nirenberg (1979). We obtain a reflectional symmetry result with respect to maxima and minima of solutions.

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Phillipo Lappicy. 2019-01-17. A symmetry property for elliptic equations on the sphere. https://arxiv.org/abs/1901.05838

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