The talk concerns bounded domains with continuous boundary. We study how the corresponding "good direction", with respect to which the boundary is locally a graph of a continuous function, varies in a neighborhood of the boundary, and thus show how such domains can be approximated both from the inside and the outside by topologically equivalent smooth domains. The good directions form a globally-defined field that carries some topological information about the domain, which we explore. Finally we describe a surprising consequence of the study, that the domain has portions of the boundary with better regularity. This is joint work with Arghir Zarnescu.
This is a joint colloquium co-sponsored by Applied Mathematics, Mathematics, and ICERM. Thursday, April 12, 2012 from 4:30-5:30pm in the lecture hall at ICERM. There will be a reception at 4pm preceding the talk.