Sharp Results for the Regularity and Stability of
the Free Boundary in the Obstacle Problem
Ivan Blank
Rutgers New Brunswick
Wednesday, February 13
2:30-3:30 pm, Room 4422
The problem of finding the smallest superharmonic function which lies
above a given obstacle and which has prescribed boundary data is called
the obstacle problem. After finding this minimizer, it is natural to
study the regularity of the boundary of the set where the solution makes
contact with the obstacle. In 1977 Caffarelli showed that for a very
natural class of obstacles, when this (free) boundary is not smooth, it
has to have a very specific geometry. This talk explores what happens to
this result when we weaken Caffarelli's hypotheses.