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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Lappicy, P. A Symmetry Property for Fully Nonlinear Elliptic Equations on the Sphere. Bull Braz Math Soc, New Series 51, 671–680 (2020). https://doi.org/10.1007/s00574-019-00168-7
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DOI: https://doi.org/10.1007/s00574-019-00168-7