{"paper":{"title":"On $p$-modulus estimates in Orlicz-Sobolev classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"R. Salimov","submitted_at":"2014-09-07T21:10:49Z","abstract_excerpt":"Under a condition of the Calderon type on $\\varphi$, we show that a homeomorphism $f$ of finite distortion in $W^{1,\\varphi}_{\\rm loc}$ and, in particular, $f\\in W^{1,q}_{\\rm loc}$ for $q>n-1$ in ${\\Bbb R}^n$, $n\\ge 3$, is a lower $Q$-homeomorphisms with respect to the $p$-modulus with $\\left[ K_{I,\\alpha}(x,f)\\right]^{\\beta}$, $p>n-1$ and a ring $Q_{*}$-homeomorphism with respect to the $\\frac{p}{p-n+1}$-modulus with $Q_{*}(x)=K_{I,\\alpha}(x,f)$ where $ K_{I,\\alpha}(x,f)$ is its inner $\\alpha$-dilatation and $\\alpha=\\frac{p}{p-n+1}$, $\\beta=\\frac{p-n+1}{n-1}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2167","kind":"arxiv","version":2},"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"}