{"paper":{"title":"Generalized convergence of solutions for nonlinear Hamilton-Jacobi equations with state-constraint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jianlu Zhang, Son Tu","submitted_at":"2023-03-29T23:19:08Z","abstract_excerpt":"For a continuous Hamiltonian $H : (x, p, u) \\in T^*\\mathbb{R}^n \\times \\mathbb{R}\\rightarrow \\mathbb{R}$, we consider the asymptotic behavior of associated Hamilton--Jacobi equations with state-constraint $H(x, Du, \\lambda u) \\leq C_\\lambda$ in $\\Omega_\\lambda\\subset \\mathbb{R}^n$ and $H(x, Du, \\lambda u) \\geq C_\\lambda$ on $\\overline{\\Omega}_\\lambda\\subset \\mathbb{R}^n$ a $\\lambda\\rightarrow 0^+$. When $H$ satisfies certain convex, coercive, and monotone conditions, the domain $\\Omega_\\lambda:=(1+r(\\lambda))\\Omega$ keeps bounded, star-shaped for all $\\lambda>0$ with $\\lim_{\\lambda\\rightarrow "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.17058","kind":"arxiv","version":3},"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/2303.17058/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"}