We show that each connected component of the boundary of a parabolic NTA domain in ℝ2 is given by a graph. We then apply this observation to classify blowup solutions in ℝ2 to a free boundary problem for caloric measure first considered by Hofmann, Lewis and Nyström .
Bibliographical noteFunding Information:
Partially supported by an NSF Graduate Research Fellowship, DGE 1144082 and the University of Chicago RTG grant DMS 1246999.
- Caloric measure
- NTA domains
- free boundary problem
- parabolic PDE