{"paper":{"title":"The Dirichlet elliptic problem involving regional fractional Laplacian","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huyuan Chen","submitted_at":"2015-09-19T01:17:42Z","abstract_excerpt":"In this paper, we consider the solutions for elliptic equations involving regional fractional Laplacian \\begin{equation}\\label{0}\n  \\arraycolsep=1pt \\begin{array}{lll}\n  \\displaystyle (-\\Delta)^\\alpha_\\Omega u=f \\qquad & {\\rm in}\\quad \\Omega,\\\\[2mm] \\phantom{ (-\\Delta)^\\alpha }\n  \\displaystyle u=g\\quad & {\\rm on}\\quad \\partial \\Omega, \\end{array} \\end{equation} where $\\Omega$ is a bounded open domain in $\\mathbb{R}^N$ ($N\\ge 2$) with $C^2$ boundary $\\partial\\Omega$,\n  $\\alpha\\in(\\frac12,1)$ and the operator $(-\\Delta)^\\alpha_\\Omega$ denotes the regional fractional Laplacian. We prove that when"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05838","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"}