{"paper":{"title":"A rigidity result for effective Hamiltonians with $3$-mode periodic potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hung V. Tran, Yifeng Yu","submitted_at":"2017-07-06T14:12:41Z","abstract_excerpt":"We continue studying an inverse problem in the theory of periodic homogenization of Hamilton-Jacobi equations proposed in [14]. Let $V_1, V_2 \\in C(\\mathbb{R}^n)$ be two given potentials which are $\\mathbb{Z}^n$-periodic, and $\\overline{H}_1, \\overline{H}_2$ be the effective Hamiltonians associated with the Hamiltonians $\\frac{1}{2}|p|^2 + V_1$, $\\frac{1}{2}|p|^2+V_2$, respectively.\n  A main result in this paper is that, if the dimension $n=2$ and each of $V_1, V_2$ contains exactly $3$ mutually non-parallel Fourier modes, then $$ \\overline H_1\\equiv \\overline H_2 \\quad \\iff \\quad V_1(x)=V_2\\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01804","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"}