Geodesic
Symmetry of solutions of semilinear elliptic problems
Journal of the European Mathematical Society, Tome 10 (2008) no. 2, pp. 439-456

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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.
DOI : 10.4171/jems/117
Classification : 35-XX, 00-XX
Keywords: Polarization, symmetrization, Steiner symmetrization, foliated Schwarz symmetrization, spherical cap symmetrization, quasi-continuous functions, intermediate value theorem, partial symmetry of solutions to semilinear elliptic equations, least-energy solut 
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     title = {Symmetry of solutions of semilinear elliptic problems},
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Jean Van Schaftingen; Michel Willem. Symmetry of solutions of semilinear elliptic problems. Journal of the European Mathematical Society, Tome 10 (2008) no. 2, pp. 439-456. doi: 10.4171/jems/117

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