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. 439–456DOI 10.4171/JEMS/117