{"paper":{"title":"A slicing approach to stress-strain duality","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Giovanni Scilla, Virginia De Cicco","submitted_at":"2026-07-19T10:45:21Z","abstract_excerpt":"The classical Kohn-Temam stress-strain pairing $({\\bf A}:E{\\bf u})$ for symmetric tensors ${\\bf A}$ and ${\\bf u}\\in BD$ is typically formulated under summability assumptions on the divergence of ${\\bf A}$. This excludes stress fields whose divergence has singular surface contributions, as occurs at cracks and material interfaces in continuum mechanics. We define and study stress-strain pairings for bounded symmetric divergence-measure tensor fields. For general ${\\bf u}\\in BD$, we introduce a slicing pairing $(({\\bf A}:E{\\bf u}))_\\Xi$ for tensor fields satisfying a directional $BV$-type condit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.17183","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/2607.17183/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"}