{"paper":{"title":"On mappings in the Orlicz-Sobolev classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Denis Kovtonyuk, Evgeny Sevost'yanov, Ruslan Salimov, Vladimir Ryazanov","submitted_at":"2010-12-22T15:31:23Z","abstract_excerpt":"First of all, we prove that open mappings in Orlicz-Sobolev classes $W^{1,\\phi}_{\\rm loc}$ under the Calderon type condition on $\\phi$ have the total differential a.e. that is a generalization of the well-known theorems of Gehring-Lehto-Menchoff in the plane and of V\\\"ais\\\"al\\\"a in ${\\Bbb R}^n$, $n\\geqslant3$. Under the same condition on $\\phi$, we show that continuous mappings $f$ in $W^{1,\\phi}_{\\rm loc}$, in particular, $f\\in W^{1,p}_{\\rm loc}$ for $p>n-1$ have the $(N)$-property by Lusin on a.e. hyperplane. Our examples demonstrate that the Calderon type condition is not only sufficient bu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5010","kind":"arxiv","version":4},"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"}