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arXiv · 1310.6845

Boundary regularity for degenerate and singular parabolic equations

Anders Björn·Jana Björn·Ugo Gianazza·Mikko Parviainen
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Abstract

We characterise regular boundary points of the parabolic $p$-Laplacian in terms of a family of barriers, both when $p>2$ and $1<p<2$. Due to the fact that $p\not=2$, it turns out that one can multiply the $p$-Laplace operator by a positive constant, without affecting the regularity of a boundary point. By constructing suitable families of barriers, we give some simple geometric conditions that ensure the regularity of boundary points.

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Anders Björn, Jana Björn, Ugo Gianazza, Mikko Parviainen. 2013-10-25. Boundary regularity for degenerate and singular parabolic equations. https://doi.org/10.1007/s00526-014-0734-9

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