{"paper":{"title":"A numerical study of the homogeneous elliptic equation with fractional order boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Petr Vabishchevich, Raytcho Lazarov","submitted_at":"2017-02-21T17:12:19Z","abstract_excerpt":"We consider the homogeneous equation ${\\mathcal A} u=0$, where ${\\mathcal A}$ is a symmetric and coercive elliptic operator in $H^1(\\Omega)$ with $\\Omega$ bounded domain in ${{\\mathbb R}}^d$. The boundary conditions involve fractional power $\\alpha$, $ 0 < \\alpha <1$, of the Steklov spectral operator arising in Dirichlet to Neumann map. For such problems we discuss two different numerical methods: (1) a computational algorithm based on an approximation of the integral representation of the fractional power of the operator and (2) numerical technique involving an auxiliary Cauchy problem for an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06477","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"}