{"paper":{"title":"A Dirichlet problem of the fractional Laplace equation in the bounded Lipschitz domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tongkeun Chang","submitted_at":"2012-05-22T06:22:10Z","abstract_excerpt":"In this paper, we study a Dirichlet problem of a fractional Laplace equation in a bounded Lipschitz domain in $ \\R, n \\geq 2$. Our main result is that for the given data $F \\in \\dot H^s(\\Om^c), 0 < s<1$, we find the function which satisfies that $\\De^s u =0$ in $\\Om$,\n  $u|_{\\Om^c} =F$ and $|u|_{\\dot{H}^s(\\R)} \\leq c |F|_{\\dot H^s(\\Om^c)}$. Furthermore, we represent the solution with an integral operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4814","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"}