{"paper":{"title":"Dirichlet-type energy of mappings between two concentric annuli","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AP","authors_text":"David Kalaj, Jiaolong Chen","submitted_at":"2020-09-28T20:43:16Z","abstract_excerpt":"Let $\\mathbb{A}$ and $\\mathbb{A_{*}}$ be two non-degenerate spherical annuli in $\\mathbb{R}^{n}$ equipped with the Euclidean metric and the weighted metric $|y|^{1-n}$, respectively. Let $\\mathcal{F}(\\mathbb{A},\\mathbb{A_{*}})$ denote the class of homeomorphisms in $\\mathcal{W}^{1,n-1}(\\mathbb{A},\\mathbb{A_{*}})$. For $n=3$, the second author \\cite{kalaj2018} proved that the minimizers of the Dirichlet-type energy $\\mathcal{E}[h]=\\int_{\\mathbb{A}} \\frac{\\|Dh(x)\\|^{n-1}}{|h(x)|^{n-1}}dx$ are certain generalized radial diffeomorphisms, where $h\\in \\mathcal{F}(\\mathbb{A},\\mathbb{A_{*}})$. For the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.13617","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2009.13617/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}