Parabolic NTA domains in $\mathbb R^2$

Max Engelstein

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arXiv · 1607.08650

Parabolic NTA domains in $\mathbb R^2$

Max Engelstein

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Abstract

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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Max Engelstein. 2016-07-28. Parabolic NTA domains in $\mathbb R^2$. https://arxiv.org/abs/1607.08650

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