Electron. J. Diff. Eqns., Vol. 2005(2005), No. 132, pp. 1-12.

Level set method for solving Poisson's equation with discontinuous nonlinearities

Joseph Kolibal

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.

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Joseph Kolibal
Department of Mathematics
University of Southern Mississippi
Hattiesburg, MS 39406, USA
email: Joseph.Kolibal@usm.edu

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