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.
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Received: 5 May 2002, Accepted: 3 September 2002, Published online: 17 December 2002
Mathematics Subject Classification (2000):
35B40 - 35J20
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Smets, D., Willem, M. Partial symmetry and asymptotic behavior for some elliptic variational problems. Cal Var 18, 57–75 (2003). https://doi.org/10.1007/s00526-002-0180-y
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DOI: https://doi.org/10.1007/s00526-002-0180-y