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2019 Boundary behavior of solutions to the parabolic $p$-Laplace equation
Benny Avelin, Tuomo Kuusi, Kaj Nyström
Anal. PDE 12(1): 1-42 (2019). DOI: 10.2140/apde.2019.12.1

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 C1,1-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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Benny Avelin. Tuomo Kuusi. Kaj Nyström. "Boundary behavior of solutions to the parabolic $p$-Laplace equation." Anal. PDE 12 (1) 1 - 42, 2019. https://doi.org/10.2140/apde.2019.12.1

Information

Received: 28 October 2015; Accepted: 10 April 2018; Published: 2019
First available in Project Euclid: 16 August 2018

zbMATH: 06930183
MathSciNet: MR3842908
Digital Object Identifier: 10.2140/apde.2019.12.1

Subjects:
Primary: 35K20
Secondary: 35B65 , 35K65

Keywords: $p$-parabolic equation , $p$-stability , boundary Harnack principle , degenerate , Intrinsic geometry , intrinsic Harnack chains , waiting time phenomenon

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 1 • 2019
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