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Symmetry Results for Positive Solutions of Some Elliptic Equations on Manifolds

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Abstract

We adapt the method of moving planes in order to obtainsymmetry results for positive solutions of some elliptic equations onmanifolds, in the case where our problem satisfies certain symmetryhypothesis. We also obtain monotonicity results using the slidingmethod.

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Authors and Affiliations

  1. Centre de Mathématiques et de Leurs Applications, CNRS UMR-8536, Ecole Normale Supérieure de Cachan, 61 Avenue du Président Wilson, 94235, Cachan Cedex, France. e-mail

    Luís Almeida

  2. Centre de Mathématiques et de Leurs Applications, CNRS UMR-8536, Ecole Normale Supérieure de Cachan, 61 Avenue du Président Wilson, 94235, Cachan Cedex, France. e-mail

    Yuxin Ge (Faculté de Sciences et Technologie)

  3. Département de Mathématiques, Université Paris XII-Val de Marne, 61, avenue du Général de Gaulle, 94010, Créteil Cedex, France

    Yuxin Ge (Faculté de Sciences et Technologie)

Authors
  1. Luís Almeida
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  2. Yuxin Ge
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Almeida, L., Ge, Y. Symmetry Results for Positive Solutions of Some Elliptic Equations on Manifolds. Annals of Global Analysis and Geometry 18, 153–170 (2000). https://doi.org/10.1023/A:1006644025734

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  • DOI: https://doi.org/10.1023/A:1006644025734

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