Symmetry of solutions of semilinear elliptic problems

Jean Van Schaftingen; Michel Willem

Journal of the European Mathematical Society (2008)

  • Volume: 010, Issue: 2, page 439-456
  • ISSN: 1435-9855

Abstract

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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.

How to cite

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Van Schaftingen, Jean, and Willem, Michel. "Symmetry of solutions of semilinear elliptic problems." Journal of the European Mathematical Society 010.2 (2008): 439-456. <http://eudml.org/doc/277807>.

@article{VanSchaftingen2008,
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.},
author = {Van Schaftingen, Jean, Willem, Michel},
journal = {Journal of the European Mathematical Society},
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; polarization; symmetrization; quasi-continuous functions; semilinear elliptic equations; least energy solutions; ground states; nodal solutions},
language = {eng},
number = {2},
pages = {439-456},
publisher = {European Mathematical Society Publishing House},
title = {Symmetry of solutions of semilinear elliptic problems},
url = {http://eudml.org/doc/277807},
volume = {010},
year = {2008},
}

TY - JOUR
AU - Van Schaftingen, Jean
AU - Willem, Michel
TI - Symmetry of solutions of semilinear elliptic problems
JO - Journal of the European Mathematical Society
PY - 2008
PB - European Mathematical Society Publishing House
VL - 010
IS - 2
SP - 439
EP - 456
AB - 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.
LA - eng
KW - 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; polarization; symmetrization; quasi-continuous functions; semilinear elliptic equations; least energy solutions; ground states; nodal solutions
UR - http://eudml.org/doc/277807
ER -

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