Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 132, pp. 1-12.

Title: Level set method for solving Poisson's equation with 
       discontinuous nonlinearities
       
Author: Joseph Kolibal (Univ. of Southern Mississippi, Hattiesburg, MS, USA)

Abstract: 
 We study semi-linear elliptic free boundary problems 
 in which the forcing term is discontinuous;
 i.e., a Poisson's equation where the  forcing term is
 the Heaviside function applied to the unknown minus a constant.
 This approach uses level sets to construct a monotonic
 sequence of iterates which converge to a class of solutions to the
 free boundary problem. The monotonicity of the construction
 based on nested sets provides insight into the connectivity of
 the free boundary sets associated with the solutions.
 
Submitted October 14, 2005. Published November 25, 2005.
Math Subject Classifications: 35J05, 35J60.
Key Words: Laplace equation; reduced wave equation (Helmholtz);
           Poisson equation;  nonlinear elliptic PDE.