{"paper":{"title":"A priori bounds for energy-bounded solutions of critical polyharmonic equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bruno Premoselli, Lorenzo Carletti","submitted_at":"2026-05-28T09:52:37Z","abstract_excerpt":"We investigate critical polyharmonic equations of the following type: $$ Lu = |u|^{2^\\sharp-2} u \\quad \\text{ in } \\Omega $$ with Dirichlet boundary conditions, in a smooth bounded domain $\\Omega$ of $\\mathbb{R}^n$. Here $L$ is an elliptic differential operator of even integer order $2 \\le 2k < n$ whose leading order term is $(-\\Delta)^k$ and $2^\\sharp = \\frac{2n}{n-2k}$ is the critical Sobolev exponent. Our main result establishes, in large dimensions, uniform \\emph{a priori} bounds on bounded-energy solutions of this problem under a coercivity assumption of sorts on the lower-order terms of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29690","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/2605.29690/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"}