Symmetry of solutions of semilinear elliptic problems
Michel Willem
Université Catholique de Louvain, BelgiumJean Van Schaftingen
Université Catholique de Louvain, Belgium

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