{"paper":{"title":"Exact relations for Green's functions in linear PDE and boundary field equalities: a generalization of conservation laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniel Onofrei, Graeme W. Milton","submitted_at":"2017-12-10T22:05:47Z","abstract_excerpt":"Many physics problems have $J(x)=L(x)E(x)+h(x)$, source $h(x)$, fields $E$,$J$ satisfying differential constraints, symbolized by $E\\in\\cal E$,$J\\in\\cal J$ where $\\cal E$,$\\cal J$ are orthogonal spaces. If $L(x)$ takes values in certain nonlinear manifolds $\\cal M$, and coercivity, boundedness hold, then the Green's function satisfies exact identities. We also link Green's functions of different problems. The analysis, based on the theory of exact relations for composites, does not assume microscale variations in $L(x)$, and allows for other equations, such as for waves in lossy media. For bod"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03597","kind":"arxiv","version":6},"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"}