Parabolic NTA domains in ℝ2

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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].

Original languageEnglish (US)
Pages (from-to)1524-1536
Number of pages13
JournalCommunications in Partial Differential Equations
Issue number10
StatePublished - Oct 3 2017
Externally publishedYes

Bibliographical note

Funding Information:
Partially supported by an NSF Graduate Research Fellowship, DGE 1144082 and the University of Chicago RTG grant DMS 1246999.

Publisher Copyright:
© 2017 Taylor & Francis.


  • Caloric measure
  • NTA domains
  • free boundary problem
  • parabolic PDE


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