{"paper":{"title":"On the Moser-Trudinger inequality in fractional Sobolev-Slobodeckij spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Bernhard Ruf, Enea Parini","submitted_at":"2016-07-26T13:17:51Z","abstract_excerpt":"We consider the problem of finding the optimal exponent in the Moser-Trudinger inequality \\[ \\sup \\left\\{\\int_\\Omega \\exp{\\left(\\alpha\\,|u|^{\\frac{N}{N-s}}\\right)}\\,\\bigg|\\,u \\in \\widetilde{W}^{s,p}_0(\\Omega),\\,[u]_{W^{s,p}(\\mathbb{R}^N)}\\leq 1 \\right\\}< + \\infty.\\] Here $\\Omega$ is a bounded domain of $\\mathbb{R}^N$ ($N\\geq 2$), $s \\in (0,1)$, $sp = N$, $\\widetilde{W}^{s,p}_0(\\Omega)$ is a Sobolev-Slobodeckij space, and $[\\cdot]_{W^{s,p}(\\mathbb{R}^N)}$ is the associated Gagliardo seminorm. We exhibit an explicit exponent $\\alpha^*_{s,N}>0$, which does not depend on $\\Omega$, such that the Mo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07681","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"}