{"paper":{"title":"Boundary integral operator for the fractional Laplacian in the bounded smooth domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tongkeun Chang","submitted_at":"2014-11-18T02:29:12Z","abstract_excerpt":"We study the boundary integral operator induced from the fractional Laplace equation in a bounded smooth domain. For $1/2 < \\alpha? < 1$, we show the bijectivity of the boundary integral operator $S_{2\\alpha} : L^p(\\partial \\Omega) \\rightarrow H^{2\\alpha-1}_p (\\partial \\Omega), 1 < p < 1$. As an application, we show the existence of the solution of the boundary value problem of the fractional Laplace equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4719","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"}