{"paper":{"title":"Quasiconvexity for the Dacorogna--Marcellini Energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Federico Pasqualotto, Giuseppe Bruno","submitted_at":"2026-08-06T17:57:45Z","abstract_excerpt":"We prove that the planar Dacorogna--Marcellini energy $f_\\gamma(A)=|A|^4-2\\gamma|A|^2\\det A$ is quasiconvex exactly when it is rank-one convex, i.e. if and only if $|\\gamma|\\leq\\frac{2}{\\sqrt3}$. The proof uses a monotonicity property of the energy functional along the componentwise heat flow. As a corollary of our method, we show that for homogeneous quartic polynomials on $2 \\times 2$ matrices invariant by left and right rotation, quasiconvexity is equivalent to rank one convexity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06367","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/2608.06367/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"}