{"paper":{"title":"A uniqueness theorem for nonvariational solutions of the Helmholtz equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"M. Lanza de Cristoforis","submitted_at":"2025-04-14T16:37:11Z","abstract_excerpt":"We consider a bounded open subset $\\Omega$ of ${\\mathbb{R}}^n$ of class $C^{1,\\alpha}$ for some $\\alpha\\in]0,1[$, and we define a distributional outward unit normal derivative for $\\alpha$-H\\\"{o}lder continuous solutions of the Helmholtz equation in the exterior of $\\Omega$ that may not have a classical outward unit normal derivative at the boundary points of $\\Omega$ and that may have an infinite Dirichlet integral around the boundary of $\\Omega$. Namely for solutions that do not belong to the classical variational setting. Then we show a Schauder boundary regularity result for $\\alpha$-H\\\"{o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.11487","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/2504.11487/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"}