{"paper":{"title":"Local and nonlocal boundary conditions for $\\mu$-transmission and fractional elliptic pseudodifferential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Gerd Grubb","submitted_at":"2014-03-27T17:26:40Z","abstract_excerpt":"A classical pseudodifferential operator $P$ on $R^n$ satisfies the $\\mu$-transmission condition relative to a smooth open subset $\\Omega $, when the symbol terms have a certain twisted parity on the normal to $\\partial\\Omega $. As shown recently by the author, the condition assures solvability of Dirichlet-type boundary problems for elliptic $P$ in full scales of Sobolev spaces with a singularity $d^{\\mu -k}$, $d(x)=\\operatorname{dist}(x,\\partial\\Omega)$. Examples include fractional Laplacians $(-\\Delta)^a$ and complex powers of strongly elliptic PDE.\n  We now introduce new boundary conditions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7140","kind":"arxiv","version":6},"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"}