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Symmetry and related properties via the maximum principle

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Abstract

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.

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Authors and Affiliations

  1. Rockefeller University, USA

    B. Gidas

  2. Courant Institute of Math. Sci., New York University, 10012, New York, NY, USA

    Wei-Ming Ni & L. Nirenberg

Authors
  1. B. Gidas
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  2. Wei-Ming Ni
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  3. L. Nirenberg
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Additional information

Communicated by A. Jaffe

Supported in part by the National Science Foundation, grant no. PHY-78-08066

Partially supported by the U.S. Army Research Office, grant no. DAA 29-78-G-0127

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Gidas, B., Ni, WM. & Nirenberg, L. Symmetry and related properties via the maximum principle. Commun.Math. Phys. 68, 209–243 (1979). https://doi.org/10.1007/BF01221125

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  • DOI: https://doi.org/10.1007/BF01221125

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