Partial symmetry and asymptotic behavior for some elliptic variational problems
- 364 Downloads
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 ) 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  inequalities.
KeywordsAsymptotic Behavior Variational Problem Type Functional Elementary Proof Partial Symmetry
Unable to display preview. Download preview PDF.
- 1.Ahlfors, L.V.: Conformal invariants. Mc Graw Hill 1973Google Scholar
- 2.Badiale, M., Tarentello, G.: A Sobolev-Hardy inequality with applications to a nonlinear elliptic equation arising in astrophysics. To appear in Arch. Rational Mech. Anal. (2001)Google Scholar
- 4.Baernstein, A., A unified approach to symmetrization. Symposia Matematica 35, 47--91 (1995)Google Scholar
- 7.Byeon, J., Wang, Z.Q.Google Scholar
- 9.Cao, D., Peng, S.: The asymptotic behaviour of the ground state solutions for Hénon equation. To appear in J. Math. Anal. Appl.Google Scholar
- 11.Catrina, F., Wang, Z.Q.: Asymptotic uniqueness and exact symmetry of k-bump solutions for a class of degenerate elliptic problems. Proc. of the Kennesaw Conference, Disc. Cont. Dyn. Syst. 80--88 (2001)Google Scholar
- 14.Hénon, M.: Numerical experiments on the stability of spherical stellar systems. Astronomy and Astrophysics 24, 229--238 (1973)Google Scholar
- 16.Pacella, F.: Symmetry results for solutions of semilinear elliptic equations with convex nonlinearities. PreprintGoogle Scholar
- 18.Secchi, S., Smets, D., Willem, M.: In preparationGoogle Scholar
- 20.Willem, M.: A decomposition lemma and applications. Proceedings of Morningside Center of Mathematics, Beijing 1999Google Scholar