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Symmetry properties of positive solutions of elliptic equations in an infinite sectorial cone*

Published online by Cambridge University Press:  14 November 2011

Chie-Ping Chu  and
Hwai-Chiuan Wang
Chie-Ping Chu
Affiliation:
Department of Mathematics, Soochow University, Taipei, Taiwan
Hwai-Chiuan Wang
Affiliation:
Department of Mathematics, Tsing Hua University, Hsinchu, Taiwan
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Synopsis

We prove symmetry properties of positive solutions of semilinear elliptic equations Δu + f(u) = 0 with Neumann boundary conditions in an infinite sectorial cone. We establish that any positive solution u of such equations in an infinite sectorial cone ∑α in ℝ3 is spherically symmetric if the amplitude α of ∑α is not greater than π.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 122 , Issue 1-2 , 1992 , pp. 137 - 160
Copyright
Copyright © Royal Society of Edinburgh 1992

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