{"paper":{"title":"Embeddings for the space $LD_\\gamma^{p}$ on sets of finite perimeter","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anna L. Mazzucato, Nikolai V. Chemetov","submitted_at":"2018-08-02T00:36:14Z","abstract_excerpt":"Given an open set with finite perimeter $\\Omega\\subset \\mathbb{R}^n$, we consider the space $LD_\\gamma^{p}(\\Omega)$, $1\\leq p<\\infty$, of functions with $p$th-integrable deformation tensor on $\\Omega$ and with $p$ th-integrable trace value on the essential boundary of $\\Omega$. We establish the continuous embedding $LD_\\gamma^{p}(\\Omega)\\subset L^{pN/(N-1)}(\\Omega)$. The space $LD_\\gamma^{p}(\\Omega)$ and this embedding arise naturally in studying the motion of rigid bodies in a viscous, incompressible fluid."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00611","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"}