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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 C^{2,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, 2010Time: 1:30 pmLocation: PPB 300 |