{"paper":{"title":"Higher integrability for measures satisfying a PDE constraint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adolfo Arroyo-Rabasa, Anna Skorobogatova, Filip Rindler, Guido De Philippis, Jonas Hirsch","submitted_at":"2021-06-06T09:58:35Z","abstract_excerpt":"We establish higher integrability estimates for constant-coefficient systems of linear PDEs\n  \\[\n  \\mathcal{A} \\mu = \\sigma,\n  \\]\n  where $\\mu \\in \\mathcal{M}(\\Omega;V)$ and $\\sigma\\in \\mathcal{M}(\\Omega;W)$ are vector measures and the polar $\\frac{\\mathrm{d} \\mu}{\\mathrm{d} |\\mu|}$ is uniformly close to a convex cone of $V$ intersecting the wave cone of $\\mathcal{A}$ only at the origin. More precisely, we prove local compensated compactness estimates of the form\n  \\[\n  \\|\\mu\\|_{\\mathrm{L}^p(\\Omega')} \\lesssim |\\mu|(\\Omega) + |\\sigma|(\\Omega), \\qquad \\Omega' \\Subset \\Omega.\n  \\]\n  Here, the ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.03077","kind":"arxiv","version":2},"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/2106.03077/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"}