{"paper":{"title":"Boundary Behavior of Subelliptic Parabolic Equations on Time-Dependent Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Elin G\\\"otmark, Marie Frentz","submitted_at":"2013-01-22T13:04:26Z","abstract_excerpt":"In this paper we study the boundary behavior of solutions of a divergence-form subelliptic heat equation in a time-varying domain \\Omega in R^{n+1}, structured on a set of vector fields X = (X_1, ... X_m) with smooth coefficients satisfying H\\\"ormander's finite rank condition. Assuming that \\Omega is an X-NTA domain, we first prove a Dahlberg type estimate comparing the X-caloric measure of \\Omega and the Green function of the subelliptic heat operator. We then prove a backward Harnack inequality, the doubling property for the X-caloric measure of \\Omega, the H\\\"older continuity at the boundar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5176","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"}