2012•arXiv (Cornell University)Open access

Regularity of the free boundary in a nonlocal one-dimensional parabolic free boundary value problem

Rossitza Semerdjieva

Abstract

We consider one-dimensional parabolic free boundary value problem with a nonlocal (integro-differential) condition on the free boundary. Results on $C^m$-regularity of the free boundary are obtained. In particular, a necessary and sufficient condition for infinite differentiability of the free boundary is given.

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Key concepts: Free boundary problem, Boundary value problem, Mixed boundary condition, Mathematical analysis, Boundary (topology), Mathematics, Robin boundary condition, Differentiable function