{"paper":{"title":"Traces for fractional Sobolev spaces with variable exponents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Julio D. Rossi, Leandro M. Del Pezzo","submitted_at":"2017-04-09T13:19:38Z","abstract_excerpt":"In this note we prove a trace theorem in fractional spaces with variable exponents. To be more precise, we show that if $p\\colon\\overline{\\Omega}\\times \\overline{\\Omega}\\to (1,\\infty)$ and $q:\\partial \\Omega \\rightarrow (1,\\infty)$ are continuous functions such that \\[\n  \\frac{(n-1)p(x,x)}{n-sp(x,x)}>q(x)\n  \\qquad \\mbox{in} \\partial \\Omega \\cap\n  \\{x\\in\\overline{\\Omega}\\colon n-sp(x,x) >0\\}, \\] then the inequality $$\n  \\Vert f\\Vert _{\\scriptstyle L^{q(\\cdot)}(\\partial \\Omega)}\n  \\leq C \\left\\{\\Vert f\\Vert _{\\scriptstyle L^{\\bar{p}(\\cdot)}(\\Omega)}+\n  [f]_{s,p(\\cdot,\\cdot)} \\right\\} $$ holds. H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02599","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"}