{"paper":{"title":"H\\\"older Continuity and Differentiability Almost Everywhere of $(K_1, K_2)$-Quasiregular Mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chao Liu, Hongya Gao, Junwei Li","submitted_at":"2018-12-19T06:51:40Z","abstract_excerpt":"This paper deals with $(K_1, K_2)$-quasiregular mappings. It is shown, by Morrey's Lemma and isoperimetric inequality, that every $(K_1, K_2)$-quasiregular mapping satisfies a H\\\"older condition with exponent $\\alpha$ on compact subsets of its domain, where \\begin{align} \\alpha=\\begin{cases} 1/K_1, & \\text{for } K_1>1, \\\\ \\text{any positive number less than } 1, & \\text{for } K_1=1 \\text{ and } K_2>0, \\\\ 1, & \\text{for } K_1=1 \\text{ and } K_2=0, \\\\ 1, & \\text{for } K_1<1,\\\\ \\end{cases} \\end{align} Differentiability almost everywhere of $(K_1, K_2)$-quasiregular mappings is also derived."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.07779","kind":"arxiv","version":3},"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"}