{"paper":{"title":"Adams-Trudinger-Moser inequalities of Adimurthi-Druet type regulated by the vanishing phenomenon and its extremals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Abiel Costa Macedo, F\\'abio Sodr\\'e Rocha, Jos\\'e Francisco de Oliveira","submitted_at":"2025-05-30T07:13:23Z","abstract_excerpt":"Let $W^{m,\\frac{n}{m}}(\\mathbb{R}^n)$ with $1\\le m < n$ be the standard higher order derivative Sobolev space in the critical exponential growth threshold. We investigate a new Adams-Adimurthi-Druet type inequality on the whole space $\\mathbb{R}^n$ which is strongly influenced by the vanishing phenomenon. Specifically, we prove\n  \\begin{equation}\\nonumber\n  \\sup_{\\underset{\\|\\nabla^{m} u\\|_{\\frac{n}{m}}^{^{\\frac{n}{m}}}+\\|u\\|_{\\frac{n}{m}}^{\\frac{n}{m}} \\leq 1}{u\\in W^{m,\\frac{n}{m}}(\\mathbb{R}^n)}} \\int_{\\mathbb{R}^n}\\Phi\\left(\\beta \\left(\\frac{1+\\alpha\\|u\\|_{\\frac{n}{m}}^{\\frac{n}{m}}}{1-\\ga"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.24297","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/2505.24297/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"}