{"paper":{"title":"Stability analysis of an inverse coefficients problem in a system of partial differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Chayma Nssibi, Houcine Meftahi","submitted_at":"2025-05-08T10:39:33Z","abstract_excerpt":"In this study, we address the inverse problem of recovering the Lam\\'e parameters ($\\lambda, \\mu$) and the density $\\rho$ of a medium from the Neumann-to-Dirichlet map for any dimension $d\\geq 2$. This inverse problem finds its motivation in the reconstruction of mechanical properties of tissues in medical diagnostics. We first assume that the Lam\\'e parameters ($\\lambda, \\mu$) are know and we look for the inverse problem of recovering the density $\\rho$. In this context, we derive a constrcutive Lipschitz stability estimate in terms of the Neumann to Dirichlet map in the case of piecewise con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.05116","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/2505.05116/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"}