Parabolic NTA domains in ℝ2

Max Engelstein

doi:10.1080/03605302.2017.1382517

Parabolic NTA domains in ℝ²

Max Engelstein

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	1524-1536
Number of pages	13
Journal	Communications in Partial Differential Equations
Volume	42
Issue number	10
DOIs	https://doi.org/10.1080/03605302.2017.1382517
State	Published - Oct 3 2017
Externally published	Yes

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.

Keywords

Caloric measure
NTA domains
free boundary problem
parabolic PDE

Publisher link

10.1080/03605302.2017.1382517

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Cite this

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abstract = "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 Nystr{\"o}m [16].",

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