{"paper":{"title":"On the upper semicontinuity of a quasiconcave functional","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Denis Serre, Luigi De Rosa, Riccardo Tione","submitted_at":"2019-06-15T09:49:45Z","abstract_excerpt":"In the recent paper \\cite{SER}, the second author proved a divergence-quasiconcavity inequality for the following functional $ \\mathbb{D}(A)=\\int_{\\mathbb{T}^n} det(A(x))^{\\frac{1}{n-1}}\\,dx$ defined on the space of $p$-summable positive definite matrices with zero divergence. We prove that this implies the weak upper semicontinuity of the functional $\\mathbb{D}(\\cdot)$ if and only if $p>\\frac{n}{n-1}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.06510","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":""},"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"}