Abstract
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.
Citation
Arshak Petrosyan. Wenhui Shi. "Parabolic boundary Harnack principles in domains with thin Lipschitz complement." Anal. PDE 7 (6) 1421 - 1463, 2014. https://doi.org/10.2140/apde.2014.7.1421
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