Petrosyan, Arshak; Shi, Wenhui Parabolic boundary Harnack principles in domains with thin Lipschitz complement. (English) Zbl 1304.35374 Anal. PDE 7, No. 6, 1421-1463 (2014). In this interesting paper the authors study forward and backward boundary Harnack principles for nonnegative solutions of the heat equation in certain domains with thin Lipschitz complement. Such free boundaries are also known as thin free boundaries and are motivated by the parabolic Signorini problem.The boundary Harnack principles give the possibility of proving that the thin Lipschitz free boundaries have Hölder-continuous spatial normals, following the original idea introduced by We have to point out that the elliptic counterparts of the results in this paper are very well known; see Athanasopoulos and Caffarelli. The authors prove two types of boundary Harnack principles for parabolic equations: the forward one (also known as the Carleson estimate) and the backward one. Reviewer: Vincenzo Vespri (Firenze) Cited in 3 Documents MSC: 35K85 Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators 35K20 Initial-boundary value problems for second-order parabolic equations 35R35 Free boundary problems for PDEs 35B45 A priori estimates in context of PDEs Keywords:backward boundary Harnack principle; parabolic Signorini problem; thin free boundaries; regularity of free boundary; Carleson estimate PDF BibTeX XML Cite \textit{A. Petrosyan} and \textit{W. Shi}, Anal. PDE 7, No. 6, 1421--1463 (2014; Zbl 1304.35374) Full Text: DOI arXiv OpenURL References: This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.