University of Washington
Talk Title: Unique Continuation on Convex Sets
Abstract: The question of how much data uniquely determines a harmonic function is a fundamental problem. By considering the difference between two harmonic functions, this is naturally equivalent to questions of how a harmonic function can vanish. For example, one of the first results in this area is the fact that a harmonic function which vanishes in an open ball must vanish identically. However, if we assume that a harmonic function vanishes continuously on a surface or on the boundary of a region, things become more complicated. In this talk, we introduce some new results about harmonic functions which vanish continuously on an open set of a convex boundary.