{"paper":{"title":"Dimension of divergence set of the wave equation","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Hyerim Ko, Sanghyuk Lee, Seheon Ham","submitted_at":"2021-02-25T06:14:02Z","abstract_excerpt":"We consider the Hausdorff dimension of the divergence set on which the pointwise convergence $\\lim_{t\\rightarrow 0} e^{it\\sqrt{-\\Delta}} f(x) = f(x)$ fails when $f \\in H^s(\\mathbb R^d)$. We especially prove the conjecture raised by Barcel\\'o, Bennett, Carbery and Rogers \\cite{BBCR} for $d=3$, and improve the previous results in higher dimensions $d\\ge4$. We also show that a Strichartz type estimate for $f\\to e^{it\\sqrt{-\\Delta}} f$ with the measure $ dt\\,d\\mu(x)$ is essentially equivalent to the estimate for the spherical average of $\\widehat \\mu$ which has been extensively studied for the Fal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.12701","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/2102.12701/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"}