{"paper":{"title":"Regularity of absolute minimizers for continuous convex Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changyou Wang, Peng Fa, Yuan Zhou","submitted_at":"2019-01-08T15:52:48Z","abstract_excerpt":"For any $n\\ge 2$, $\\Omega\\subset\\rn$, and any given convex and coercive Hamiltonian function $H\\in C^{0}(\\rn)$, we find an optimal sufficient condition on $H$, that is, for any $c\\in\\mathbb R$, the level set $H^{-1}(c)$ does not contains any line segment, such then any absolute minimizer $u\\in AM_H(\\Omega)$ enjoys the linear approximation property. As consequences, we show that when $n=2$, if $u\\in AM_H(\\Omega)$ then $u\\in C^1$; and if $u\\in AM_H(\\rr^2)$ satisfies a linear growth at the infinity, then $u$ is a linear function on $\\rr^2$. In particular, if $H$ is a strictly convex Banach norm $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02379","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"}