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  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 131, Issue 4
  • August 2001, pp. 967-985

On a class of elliptic problems in R2: symmetry and uniqueness results

  • J. Prajapat (a1) and G. Tarantello (a2)
  • DOI:
  • Published online: 12 July 2007

In the plane R2, we classify all solutions for an elliptic problem of Liouville type involving a (radial) weight function. As a consequence, we clarify the origin of the non-radially symmetric solutions for the given problem, as established by Chanillo and Kiessling.

For a more general class of Liouville-type problems, we show that, rather than radial symmetry, the solutions always inherit the invariance of the problem under inversion with respect to suitable circles. This symmetry result is derived with the help of a 'shrinking-sphere' method.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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