Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 44, pp. 1-11.

Title: Symmetry theorems via the continuous steiner symmetrization

Author: L. Ragoub (Riyadh College of Technology, Riyadh, Saudi Arabia)
    
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 $\Omega$ 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.
 
Submitted  October 1, 1999. Published June 12, 2000.
Math Subject Classifications: 28D10, 35B05, 35B50, 35J25, 35J60, 35J65.
Key Words: Moving plane method; Steiner Symmetrization; 
           Overdetermined problems; Local Symmetry.