✦ LIBER ✦
Symmetry Properties for Positive Solutions to Some Elliptic Equations in Sector Domains with Large Amplitude
✍ Scribed by Meijun Zhu
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 82 KB
- Volume
- 261
- Category
- Article
- ISSN
- 0022-247X
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✦ Synopsis
In this paper we study symmetry properties for positive solutions of semilinear elliptic equation u + f u = 0 with mixed boundary condition in a spherical sector α R , where α, the amplitude of the sector, is between π and 2π. Under certain conditions on f u , we prove that all positive solutions are radially symmetric about the origin. Unlike well-known results of B. Gidas et al. (1979, Comm. Math. Phys. 68, 209-243) on Dirichlet problem, or early results of Berestycki and Pacella on the same problem for α R with an acute angle, extra conditions on f u are needed, as pointed out early by H.