Free Boundary Problems and Density Perimeter

Convexity of the Free Boundary for an Exterior Free Boundary Problem Involving the Perimeter

We prove that if the given compact set K is convex then a minimizer of the functional I(v) = ∫ BR |∇v|dx + Per({v > 0}), 1 < p < ∞, over the set {v ∈ H 0 (BR)| v ≡ 1 on K ⊂ BR} has a convex support, and as a result all its level sets are convex as well. We derive the free boundary condition for the minimizers and prove that the free boundary is analytic and the minimizer is unique.

On Free Boundary Problems

Free Boundary Problems

Paradigmatic examples are the classical Stefan problem and more general models of phase transitions, where the free boundary is the moving interface between phases. Other examples come from problems in surface science, plastic molding and glass rolling, filtration through porous media, where free boundaries occur as fronts between saturated and unsaturated regions, and others from reaction-diff...

Free Boundary Problems and Perpetual American Strangles

We consider the perpetual American strangles in the geometric jump-diffusion models. We assume further that the jump distribution is a mixture of exponential distributions. To solve the corresponding optimal stopping problem for this option, by using the approach in [5], we derive a system of equations that is equivalent to the associated free boundary problem with smooth pasting condition. We ...

Nahm’s equations and free boundary problems

In [4], following up work of Hitchin [9], the author found it useful to express Nahm’s equations, for a matrix group, in terms of the motion of a particle in a Riemannian symmetric space, subject to a potential field. This point of view lead readily to an elementary existence theorem for solutions of Nahm’s equation, corresponding to particle paths with prescribed end points. The original motiv...