{"paper":{"title":"Parabolic Boundary Harnack Principles in Domains with Thin Lipschitz Complement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Arshak Petrosyan, Wenhui Shi","submitted_at":"2014-01-29T17:29:17Z","abstract_excerpt":"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 $E=\\{(x,t): x_{n-1}\\leq f(x'',t),x_n=0\\}\\subset \\mathbb{R}^{n-1}\\times\\mathbb{R} $ for parabolically Lipschitz functions $f$ on $\\mathbb{R}^{n-2}\\times\\mathbb{R}$. We are motivated by applications to parabolic free boundary problems with thin (i.e co-dimension two) free boundaries. In particular, at the end of the paper we show how to prove the spatial $C^{1,\\alpha}$ regularity of the free boundary in the parab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7599","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}