{"paper":{"title":"Jensen Deficits for Inhomogeneous Monge-Amp\\`ere Dirichlet Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CV","authors_text":"Frank Wikstr\\\"om","submitted_at":"2026-06-08T13:46:26Z","abstract_excerpt":"We develop an inhomogeneous form of Edwards' Jensen-measure duality for Perron envelopes constrained by Monge--Amp\\`ere lower bounds. The admissible subsolution families are convex but not cones; nevertheless, the dual measures remain the homogeneous Jensen measures, and the right-hand side enters through a scalar Jensen deficit \\[\n  B_{\\mathcal{A}}(x,\\mu) =\n  \\inf_{u\\in\\mathcal{A}}\n  \\left(\\int_{\\partial\\Omega}u\\,d\\mu-u(x)\\right). \\] Under natural structural hypotheses we prove a boundary dual formula \\[\n  \\sup\\{u(x):u\\in\\mathcal{A},\\ u\\leq\\varphi\\text{ on }E\\}\n  =\n  \\inf_{\\mu\\in J_x^\\partial"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09492","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/2606.09492/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"}