{"paper":{"title":"Rellich type theorem and unique continuation property for discrete Maxwell operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hiroshi Isozaki, I2M), Olivier Poisson (AMU SCI","submitted_at":"2024-12-16T08:54:48Z","abstract_excerpt":"We study the Rellich type theorem (RT) for the Maxwell operator __ D = D____0 on Z3 in a constant anisotropic medium, i.e., the permittivity and permeability of which are constant non-scalar diagonal matrices. We also prove the unique continuation property (UCP) in the exterior of a compact convex set Kint $\\subset$ Z3 for the perturbed Maxwell operator __ Dp = D__p __0 on Z3 for which the permittivity and permeability are locally perturbed from a constant matrix on a compact subset in Kint ."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.11568","kind":"arxiv","version":2},"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/2412.11568/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"}