Geodesic
Symmetry theorems via the continuous Steiner symmetrization
Electronic Journal of Differential Equations, Tome 2000 (2000).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Using a new approach due to F. Brock called the Steiner symmetrization, we show first that if $u$ is a solution of an overdetermined problem in the divergence form satisfying the Neumann and non-constant Dirichlet boundary conditions, then $\Omega$ is an N-ball. In addition, we show that we can relax the condition on the value of the Dirichlet boundary condition in the case of superharmonicity. Finally, we give an application to positive solutions of some semilinear elliptic problems in symmetric domains for the divergence case.
Classification : 28D10, 35B05, 35B50, 35J25, 35J60, 35J65
Keywords: moving plane method, Steiner symmetrization, overdetermined problems, local symmetry 
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     author = {Ragoub, L.},
     title = {Symmetry theorems via the continuous {Steiner} symmetrization},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2000},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a15/}
}
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Ragoub, L. Symmetry theorems via the continuous Steiner symmetrization. Electronic Journal of Differential Equations, Tome 2000 (2000). http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a15/