{"paper":{"title":"Convergence Rates for Vanishing Viscosity Approximations of Possibly Degenerate Viscous Hamilton--Jacobi Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Junkai Qi","submitted_at":"2026-07-06T15:02:56Z","abstract_excerpt":"We study quantitative convergence rates for vanishing viscosity approximations of possibly degenerate viscous Hamilton--Jacobi equations on the flat torus. The limiting equation contains a spatially dependent diffusion coefficient a(x) >= 0, which is allowed to vanish. Under standard structural assumptions on the Hamiltonian, we first prove a pointwise convergence rate of order O(epsilon |log epsilon|). We then show that, when the error is tested against a smooth probability density, the logarithmic loss can be removed and an averaged O(epsilon) rate holds. The proof is based on the nonlinear "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05186","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/2607.05186/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"}