JournalsjemsVol. 10, No. 2pp. 439–456

Symmetry of solutions of semilinear elliptic problems

  • Michel Willem

    Université Catholique de Louvain, Belgium

  • Jean Van Schaftingen

    Université Catholique de Louvain, Belgium
Symmetry of solutions of semilinear elliptic problems cover
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Abstract

We study symmetry properties of least energy positive or nodal solutions of semilinear elliptic problems with Dirichlet or Neumann boundary conditions. The proof is based on symmetrizations in the spirit of Bartsch, Weth and Willem (J. Anal. Math., 2005) together with a strong maximum principle for quasi-continuous functions of Ancona and an intermediate-value property for such functions.

Cite this article

Michel Willem, Jean Van Schaftingen, Symmetry of solutions of semilinear elliptic problems. J. Eur. Math. Soc. 10 (2008), no. 2, pp. 439–456

DOI 10.4171/JEMS/117