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Partial symmetry and asymptotic behavior for some elliptic variational problems

  • Didier Smets
  • Michel Willem
Original Paper

Abstract.

A short elementary proof based on polarizations yields a useful (new) rearrangement inequality for symmetrically weighted Dirichlet type functionals. It is then used to answer some symmetry related open questions in the literature. The non symmetry of the Hénon equation ground states (previously proved in [19]) as well as their asymptotic behavior are analyzed more in depth. A special attention is also paid to the minimizers of the Caffarelli-Kohn-Nirenberg [8] inequalities.

Keywords

Asymptotic Behavior Variational Problem Type Functional Elementary Proof Partial Symmetry 
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

© Springer-Verlag Berlin/Heidelberg 2003

Authors and Affiliations

  1. 1.Laboratoire Jacques-Louis LionsUniversité de Paris 6ParisFrance

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