{"paper":{"title":"Geometric Criteria for Morrey Admissibility via the Real Log-Canonical Threshold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AP","authors_text":"Andr\\'ea Prokopczyk, Nivaldo Grulha","submitted_at":"2026-07-16T13:42:48Z","abstract_excerpt":"In this work we study the local well-posedness of aggregation equations in Morrey spaces for interaction kernels with an isolated analytic singularity at the origin. The velocity field is given by a nonlocal convolution involving the gradient of the kernel. We assume that, near the singularity, the gradient of the kernel is analytically comparable -- in the two-sided sense -- to a negative power of a real-analytic function with an isolated zero.\n  Under this assumption, we give a complete geometric characterisation of the admissible range of Morrey exponents: $\\nabla K \\in L^p_{\\mathrm{loc}}$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14991","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/2607.14991/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"}