Communications in Mathematical Physics

, Volume 68, Issue 3, pp 209–243 | Cite as

Symmetry and related properties via the maximum principle

  • B. Gidas
  • Wei-Ming Ni
  • L. Nirenberg


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.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Maximum Principle 
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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • B. Gidas
    • 1
  • Wei-Ming Ni
    • 2
  • L. Nirenberg
    • 2
  1. 1.Rockefeller UniversityUSA
  2. 2.Courant Institute of Math. Sci.New York UniversityNew YorkUSA

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