Analysis & PDE
- Anal. PDE
- Volume 7, Number 6 (2014), 1421-1463.
Parabolic boundary Harnack principles in domains with thin Lipschitz complement
We prove forward and backward parabolic boundary Harnack principles for nonnegative solutions of the heat equation in the complements of thin parabolic Lipschitz sets given as subgraphs
for parabolically Lipschitz functions on .
We are motivated by applications to parabolic free boundary problems with thin (i.e., codimension-two) free boundaries. In particular, at the end of the paper we show how to prove the spatial -regularity of the free boundary in the parabolic Signorini problem.
Anal. PDE, Volume 7, Number 6 (2014), 1421-1463.
Received: 8 December 2013
Accepted: 27 August 2014
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35K20: Initial-boundary value problems for second-order parabolic equations
Secondary: 35R35: Free boundary problems 35K85: Linear parabolic unilateral problems and linear parabolic variational inequalities [See also 35R35, 49J40]
Petrosyan, Arshak; Shi, Wenhui. Parabolic boundary Harnack principles in domains with thin Lipschitz complement. Anal. PDE 7 (2014), no. 6, 1421--1463. doi:10.2140/apde.2014.7.1421. https://projecteuclid.org/euclid.apde/1513731588