{"paper":{"title":"Min-max formulas and other properties of certain classes of nonconvex effective Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","math.PR"],"primary_cat":"math.AP","authors_text":"Hung V. Tran, Jianliang Qian, Yifeng Yu","submitted_at":"2017-01-04T16:31:36Z","abstract_excerpt":"This paper is the first attempt to systematically study properties of the effective Hamiltonian $\\overline{H}$ arising in the periodic homogenization of some coercive but nonconvex Hamilton-Jacobi equations. Firstly, we introduce a new and robust decomposition method to obtain min-max formulas for a class of nonconvex $\\overline{H}$. Secondly, we analytically and numerically investigate other related interesting phenomena, such as \"quasi-convexification\" and breakdown of symmetry, of $\\overline{H}$ from other typical nonconvex Hamiltonians. Finally, in the appendix, we show that our new method"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01065","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"}