Parabolic NTA domains in mathbb R²
classification
🧮 math.AP
math.CA
keywords
mathbbboundaryparabolicapplyblowupcaloricclassifycomponent
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We show that each connected component of the boundary of a parabolic NTA domain in $\mathbb R^2$ is given by a graph. We then apply this observation to classify blowup solutions in $\mathbb R^2$ to a free boundary problem for caloric measure first considered by Hofmann, Lewis and Nystr\"om (Duke Math J. 2004).
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