{"paper":{"title":"Existence, uniqueness and characterisation of vector-valued absolute minimisers for a second order $L^\\infty$-variational problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Existence, uniqueness and PDE characterisation hold for vector-valued absolute minimisers of a second-order L^∞ variational problem with a general linear elliptic operator.","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nikos Katzourakis, Roger Moser, Simone Carano","submitted_at":"2025-04-05T14:02:53Z","abstract_excerpt":"We study a vectorial $L^\\infty$-variational problem of second order, where the supremal functional depends on the vector function $u$ through a linear elliptic operator in divergence form. We prove existence and uniqueness of the minimiser $u_\\infty$ under prescribed Dirichlet boundary conditions, together with a characterisation of $u_\\infty$ as solution of a specific system of PDEs. Our result can be seen as a twofold extension of the one in Katzourakis-Moser (ARMA 2019): we generalise it to the vectorial setting and, at the same time, we consider more general elliptic operators in place of "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove existence and uniqueness of the minimiser u_∞ under prescribed Dirichlet boundary conditions, together with a characterisation of u_∞ as solution of a specific system of PDEs.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The supremal functional is defined through a linear elliptic operator in divergence form acting on the vector function u (abstract, paragraph 2).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Proves existence, uniqueness and PDE characterization of vector-valued absolute minimisers for a second-order L^∞ variational problem with general elliptic operators, extending a 2019 scalar result.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Existence, uniqueness and PDE characterisation hold for vector-valued absolute minimisers of a second-order L^∞ variational problem with a general linear elliptic operator.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"85659feddc3725af8ca221bce8fdb1f9e47c8aed0d64e28af2a687c27e40311a"},"source":{"id":"2504.04181","kind":"arxiv","version":3},"verdict":{"id":"e5bdf157-d333-4b5e-8a65-a3437bea1c44","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-22T21:27:58.440718Z","strongest_claim":"We prove existence and uniqueness of the minimiser u_∞ under prescribed Dirichlet boundary conditions, together with a characterisation of u_∞ as solution of a specific system of PDEs.","one_line_summary":"Proves existence, uniqueness and PDE characterization of vector-valued absolute minimisers for a second-order L^∞ variational problem with general elliptic operators, extending a 2019 scalar result.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The supremal functional is defined through a linear elliptic operator in divergence form acting on the vector function u (abstract, paragraph 2).","pith_extraction_headline":"Existence, uniqueness and PDE characterisation hold for vector-valued absolute minimisers of a second-order L^∞ variational problem with a general linear elliptic operator."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.04181/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"}