Symmetry Theorems via the Continuous Steiner Symmetrization
Date
2000-06-12
Authors
Ragoub, L.
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
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 Ω 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.
Description
Keywords
Moving plane method, Steiner symmetrization, Overdetermined problems, Local symmetry
Citation
Ragoub, L. (2000). Symmetry theorems via the continuous steiner symmetrization. <i>Electronic Journal of Differential Equations, 2000</i>(44), pp. 1-11.
Rights
Attribution 4.0 International