{"paper":{"title":"Rate of convergence in periodic homogenization of Hamilton-Jacobi equations: the convex setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.OC"],"primary_cat":"math.AP","authors_text":"Hiroyoshi Mitake, Hung V. Tran, Yifeng Yu","submitted_at":"2018-01-01T04:19:55Z","abstract_excerpt":"We study the rate of convergence of $u^\\epsilon$, as $\\epsilon \\to 0+$, to $u$ in periodic homogenization of Hamilton-Jacobi equations. Here, $u^\\epsilon$ and $u$ are viscosity solutions to the oscillatory Hamilton-Jacobi equation and its effective equation \\begin{equation*} {\\rm (C)_\\epsilon} \\qquad \\begin{cases} u_t^\\epsilon+H\\left(\\frac{x}{\\epsilon},Du^\\epsilon\\right)=0 \\qquad &\\text{in} \\ \\mathbb{R}^n \\times (0,\\infty), u^\\epsilon(x,0)=g(x) \\qquad &\\text{on} \\ \\mathbb{R}^n, \\end{cases} \\end{equation*} and \\begin{equation*} {\\rm (C)} \\qquad \\begin{cases} u_t+\\overline{H}\\left(Du\\right)=0 \\q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00391","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":""},"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"}