{"paper":{"title":"A quantative Sobolev regularity for absolute minimizers involving Hamiltonian $H(p)\\in C^0 (\\mathbb{R}^2)$ in plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Peng Fa, Qianyun Miao, Yuan Zhou","submitted_at":"2019-01-28T07:51:03Z","abstract_excerpt":"Suppose that $H \\in C^0 (\\mathbb{R}^2)$ satisfies \\begin{enumerate} \\item[(H1)] $H$ is locally strongly convex and locally strongly concave in $\\rr^2$, \\item[(H2)] $H(0)=\\min_{p\\in\\rr^2}H(p)=0$. \\end{enumerate} Let $\\Omega\\subset \\rr^2$ be any domain. For any $u$ absolute minimizer for $H$ in $\\Omega$, or if $H\\in C^1(\\rr^2)$ additionally, for any viscosity solution to the Aronsson equation $$\\mathscr A_H[u]=\\sum_{i,j=1}^2 H_{p_i}(Du) H_{p_j}(Du)u_{x_ix_j}=0 \\quad \\mbox{ in $\\Omega$,}$$ the following are proven in this paper: \\begin{enumerate}\n  \\item[(i)] We have\n  $[H(Du)]^\\alpha\\in W^{1,2}_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.09539","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"}