{"paper":{"title":"Rigidity and flatness of the image of certain classes of mappings having tangential Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Birzhan Ayanbayev, Hussien Abugirda, Nikos Katzourakis (Reading, UK)","submitted_at":"2017-04-14T17:47:20Z","abstract_excerpt":"In this paper we consider the PDE system of vanishing normal projection of the Laplacian for $C^2$ maps $u : \\mathbb{R}^n \\supseteq \\Omega \\longrightarrow \\mathbb{R}^N$: \\[ [\\![\\mathrm{D} u]\\!]^\\bot \\Delta u = 0 \\ \\, \\text{ in }\\Omega. \\] This system has discontinuous coefficients and geometrically expresses the fact that the Laplacian is a vector field tangential to the image of the mapping. It arises as a constituent component of the $p$-Laplace system for all $p\\in [2,\\infty]$. For $p=\\infty$, the $\\infty$-Laplace system is the archetypal equation describing extrema of supremal functionals "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04492","kind":"arxiv","version":3},"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"}