A symmetry result for an overdetermined elliptic problem using continuous rearrangement and domain derivative |
| |
Authors: | F Brock A Henrot |
| |
Institution: | (1) Dept. of Mathematics, University of Missouri-Columbia, 65211 Columbia, MO, U.S.A.;(2) Institut Elie Cartan Nancy, Universite Henri Poincare Nancy 1, B.P. 239, 54506 Vandoeuvre les Nancy Cedex, France |
| |
Abstract: | We develop a new method to prove symmetry results for overdetermined boundary value problems. This method is based on the use of continuous Steiner symmetrization together with derivative with respect to the domain. It allows to consider nonlinear equations in divergence form with dependence inr=|x| in the nonlinearity. By using the notion of “local symmetry” introduced by the first author, we prove that the domain is necessarily a ball. We also give an example where the solution of the overdetermined problem is not radially symmetric. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|