{"paper":{"title":"Almost Lipschitz regularity for solutions of elliptic equations with discontinuous coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonio Giuseppe Grimaldi, Raffaella Giova, Stefania Russo","submitted_at":"2026-06-25T06:08:40Z","abstract_excerpt":"We are interested in the local higher integrability of solutions to elliptic equations with linear growth of the form\n  $$-\\text{ div}A(x,Du)=f(x). $$ Under a Besov regularity assumption both on the partial map $x \\mapsto A(x,\\xi)$ and the datum $f$, we prove that the solutions are almost Lipschitz continuous, i.e. their gradients belong locally to $L^q$, for any finite exponent $q$. In turn, solutions are locally $\\gamma$-H\\\"older continuous, for every $\\gamma \\in (0,1)$. The difficulty arising from the lack of an explicit second variation for the problem is overcome by testing the equation w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26642","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/2606.26642/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"}