Symmetry Theorems via the Continuous Steiner Symmetrization
Southwest Texas State University, Department of Mathematics
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.
Moving plane method, Steiner symmetrization, Overdetermined problems, Local symmetry
Ragoub, L. (2000). Symmetry theorems via the continuous steiner symmetrization. <i>Electronic Journal of Differential Equations, 2000</i>(44), pp. 1-11.
Attribution 4.0 International