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Journal d’Analyse Mathématique

, Volume 81, Issue 1, pp 111–137 | Cite as

Nonlinear PDE with vector fields

  • David Holcman
Article

Abstract

A nonlinear PDE on a compact manifold is proposed where we use a given vector field. The nonlinear term involves the critical Sobolev exponent growth. To obtain the existence of solutions, conditions linking a critical point of the field and the scalar curvature are found. The second point is devoted to studying the viscosity limit of the solutions when the Laplacian term tends to zero.

Keywords

Vector Field Scalar Curvature Minimum Point Sobolev Inequality Mountain Pass 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University of Jerusalem 2000

Authors and Affiliations

  • David Holcman
    • 1
  1. 1.Mathematical Physics and Geometry of Partial Differential EquationsUniversité Pierre et Marie Curie (Paris VI)Paris Cedex 05France

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