{"paper":{"title":"Exact Green's formula for the fractional Laplacian and perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Gerd Grubb","submitted_at":"2019-04-07T13:15:25Z","abstract_excerpt":"Let $\\Omega $ be an open, smooth, bounded subset of $ \\Bbb R ^n$. In connection with the fractional Laplacian $(-\\Delta )^a$ ($a>0$), and more generally for a $2a$-order classical pseudodifferential operator ($\\psi $do) $P$ with even symbol, one can define the Dirichlet value $\\gamma _0^{a-1}u$ resp. Neumann value $\\gamma _1^{a-1}u$ of $u(x)$ as the trace resp. normal derivative of $u/d^{a-1}$ on $\\partial\\Omega $, where $d(x)$ is the distance from $x\\in\\Omega $ to $\\partial\\Omega $; they define well-posed boundary value problems for $P$.\n  A Green's formula was shown in a preceding paper, con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03648","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1904.03648/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}