Abstract
We study the existence, uniqueness and regularity of solutions of the equation f t = Δ p f = div (|Df|p-2 Df) under over-determined boundary conditions f = 0 and |Df| = 1. We show that if the initial data is concave and Lipschitz with a bounded and convex support, then the problem admits a unique solution which exists until vanishing identically. Furthermore, the free-boundary of the support of f is smooth for all positive time.
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