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manuscripta mathematica

, Volume 115, Issue 2, pp 239–258 | Cite as

Symmetry properties of solutions of semilinear elliptic equations in the plane

  • Alessio Porretta
  • Laurent Véron
Article

Abstract.

If g is a nondecreasing nonnegative continuous function we prove that any solution of −Δu+g(u)=0 in a half plane which blows-up locally on the boundary, in a fairly general way, depends only on the normal variable. We extend this result to problems in the complement of a disk. Our main application concerns the exponential nonlinearity g(u)=e au , or power–like growths of g at infinity. Our method is based upon a combination of the Kelvin transform and moving plane method.

Keywords or Phrases

Elliptic equations Kelvin transform Asymptotic expansions 

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Notes

Acknowledgments.

This research has been conducted while the first author was visiting Université de Tours in the framework of the European Project “Nonlinear Parabolic Partial Differential Equations Describing Front Propagation and Other Singular Phenomena”, RTN contract: HPRN-CT-2002-00274.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Alessio Porretta
    • 1
  • Laurent Véron
    • 2
  1. 1.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomaItalia
  2. 2.Laboratoire de Mathématiques et Physique Théorique, CNRS UMR 6083Université François RabelaisToursFrance

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