Parabolic NTA domains in $\mathbb R^2$

Max Engelstein

Parabolic NTA domains in $\mathbb R^2$

Analysis of PDEs 2017-09-19 v2 Classical Analysis and ODEs

Authors: Max Engelstein

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).

Cite

@article{arxiv.1607.08650,
  title  = {Parabolic NTA domains in $\mathbb R^2$},
  author = {Max Engelstein},
  journal= {arXiv preprint arXiv:1607.08650},
  year   = {2017}
}

Comments

12 pages, 2 figures. This version has minor revisions as suggested by a referee

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