Parabolic NTA domains in ℝ2
Max Engelstein · Communications in Partial Differential Equations · 2017
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 [16 Hofmann, S., Lewis, J.L., Nyström, K. (2004). Caloric measure in parabolic flat domains. Duke Math. J. 122(2):281–346. MR 2053754 (2005e:35092)[Crossref], [Web of Science ®] , [Google Scholar]].