Symmetry and related properties via the maximum principle

B. Gidas, Wei Ming Ni, L. Nirenberg

Research output: Contribution to journalArticlepeer-review

1855 Scopus citations


We prove symmetry, and some related properties, of positive solutions of second order elliptic equations. Our methods employ various forms of the maximum principle, and a device of moving parallel planes to a critical position, and then showing that the solution is symmetric about the limiting plane. We treat solutions in bounded domains and in the entire space.

Original languageEnglish (US)
Pages (from-to)209-243
Number of pages35
JournalCommunications in Mathematical Physics
Issue number3
StatePublished - Oct 1 1979

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