# 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

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topVan 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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