Symmetry and Asymmetry: the Method of Moving Spheres

@inproceedings{Jin2007SymmetryAA,
  title={Symmetry and Asymmetry: the Method of Moving Spheres},
  author={Qinian Jin and Yanyan Li and H. M. Xu},
  year={2007}
}
Through the work of Obata [25], Gidas-Ni-Nirenberg [10] and Caffarelli-GidasSpruck [6], the asymptotic behavior of solutions of (1.1) as well as the classification of global solutions are well understood in the case when c = 0. In [28] Véron raised the following question: For c ∈ R, c 6= 0 and n ≥ 3, let u ∈ C∞(Rn\{0}) satisfy (1.1). Is it true that u must be radially symmetric about the origin? He pointed out that there might be non-radial solutions of certain form as suggested in section 4 of… CONTINUE READING

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References

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Showing 1-10 of 32 references

A global theorem for nonlinear eigenvalue problems and applications

  • P. H. Rabinowitz
  • Contributions to Nonlinear Function Analysis…
  • 1971
Highly Influential
5 Excerpts

Uniqueness of solutions to the mean field equations for the spherical Onsager vortex

  • C.-S. Lin
  • Arch. Ration. Mech. Anal. 153
  • 2000
Highly Influential
3 Excerpts

The conjecture on conformal transformations of Riemannian manifolds

  • M. Obata
  • J. Diff. Geom. 6
  • 1971
Highly Influential
4 Excerpts

Yamabe equations on half-spaces

  • G. Bianchi, X. B. Pan
  • Nonlinear Analysis 37
  • 1999
Highly Influential
3 Excerpts

Symmetry and related properties via the maximum principle

  • B. Gidas, W.-M. Ni, L. Nirenberg
  • Comm. Math. Phys. 68
  • 1979
Highly Influential
3 Excerpts

A Kazdan-Warner type identity for the σk curvature

  • Z.-C. Han
  • C. R. Math. Acad. Sci. Paris 342
  • 2006
3 Excerpts

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