A singular integral approach to a two-phase free boundary problem

Tuesday, September 1, 2015 - 2:00pm
Math Sci 111
Simon Bortz
(MU Math)

The connection between the regularity of the (log of the) Poisson kernel and the regularity of the boundary of a given domain has been studied somewhat extensively. We will study this connection through the use of the single layer potential associated to the domain, the tools may be somewhat familiar to someone who studies PDE's using singular integrals (layer potential methods). Our method (at the present moment) can only be used in two phase problems. This is joint work with Steve Hofmann.

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