Avelin, B., Kuusi, T., Nyström, K. (2019) Boundary behavior of solutions to the parabolic p-Laplace equation. Analysis and PDE, 12 (1), 1-42. doi:10.2140/apde.2019.12.1

### Boundary behavior of solutions to the parabolic p-Laplace equation

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Author: Avelin, Benny1; Kuusi, Tuomo2; Nyström, Kaj1
Organizations: 1Department of Mathematics, Uppsala University, Uppsala, Sweden
2Department of Mathematical Sciences, University of Oulu, Oulu, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.5 MB)
Language: English
Published: Mathematical Sciences Publishers, 2018
Publish Date: 2019-10-15
Description:

# Abstract

We establish boundary estimates for nonnegative solutions to the p-parabolic equation in the degenerate range p > 2. Our main results include new parabolic intrinsic Harnack chains in cylindrical NTA domains together with sharp boundary decay estimates. If the underlying domain is $$C^{1,1}$$-regular, we establish a relatively complete theory of the boundary behavior, including boundary Harnack principles and Hölder continuity of the ratios of two solutions, as well as fine properties of associated boundary measures. There is an intrinsic waiting-time phenomenon present which plays a fundamental role throughout the paper. In particular, conditions on these waiting times rule out well-known examples of explicit solutions violating the boundary Harnack principle.

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Series: Analysis & PDE
ISSN: 2157-5045
ISSN-E: 1948-206X
ISSN-L: 2157-5045
Volume: 12
Issue: 1
Pages: 1 - 42
DOI: 10.2140/apde.2019.12.1