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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Nestor Guillen
University of Texas at Austin.
Title: Instantaneous regularization phenomena for the Stefan problem with Gibbs-Thomson law

Abstract: The two-phase Stefan problem is expected to exhibit waiting time phenomena; in other words, an initial Lipschitz free boundary might remain just Lipschitz for some positive time. On the other hand, adding a Gibbs-Thomson correction term to the model is believed to stabilize the interface and make it more regular. I will present a partial result in this direction, namely I will show that free boundaries which are Lipschitz in space and time are actually C2,α in space and become so instantaneously. This will follow first from observing that the De Giorgi-Moser-Nash theory for parabolic equations works even when one has a singular right hand side and secondly from the regularity theory for almost-minimal boundaries of Almgren, De Giorgi and Tamanini.

Date: Tuesday, April 13, 2010
Time: 1:30 pm
Location: PPB 300