{"paper":{"title":"Lipschitz stability for determination of states and inverse source problem for the mean field game equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hongyu Liu, Masahiro Yamamoto, Oleg Imanuvilov","submitted_at":"2023-04-13T17:00:37Z","abstract_excerpt":"We consider solutions satisfying the zero Neumann boundary condition and a linearized mean field game equation in $\\Omega \\times (0,T)$ whose principal coefficients depend on the time and spatial variables with general Hamiltonian, where $\\Omega$ is a bounded domain in $\\Bbb R^d$ and $(0,T)$ is the time interval. We first prove the Lipschitz stability in $\\Omega \\times (\\varepsilon, T-\\varepsilon)$ with given $\\varepsilon>0$ for the determination of the solutions by Dirichlet data on arbitrarily chosen subboundary of $\\partial\\Omega$. Next we prove the Lipschitz stability for an inverse proble"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.06673","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/2304.06673/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"}