{"paper":{"title":"Homogenization of a transmission problem with Hamilton-Jacobi equations and a two-scale interface. Effective transmission conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nicoletta Tchou (IRMAR), Yves Achdou (LJLL)","submitted_at":"2017-07-06T08:26:16Z","abstract_excerpt":"We consider a family of optimal control problems in the plane with dynamics and running costs possibly discontinuous across a two-scale oscillatory interface. Typically, the amplitude of the oscillations is of the order of $\\epsilon$ while the period is of the order of $\\epsilon$ 2. As $\\epsilon$ $\\rightarrow$ 0, the interfaces tend to a straight line $\\Gamma$. We study the asymptotic behavior of the value function as $\\epsilon$ $\\rightarrow$ 0. We prove that the value function tends to the solution of Hamilton-Jacobi equations in the two half-planes limited by $\\Gamma$, with an effective tran"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02864","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":""},"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"}