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Analysis Seminar

Tuesday, April 18, 2017 - 3:00pm

Hector Chang-Lara

Columbia University


University of Pennsylvania


We propose a method to determine the smoothness for the free boundary of sufficiently flat solutions of one phase Hele-Shaw problems. The novelty is the observation that under a flatness assumption the free boundary–represented by the hodograph transform of the solution--solves a nonlinear integro-differential equation. This nonlinear equation can be linearized to a (nonlocal) parabolic equation with bounded measurable coefficients, for which regularity estimates are available. This is joint work with N. Guillen.