{"paper":{"title":"Everywhere differentiability of viscosity solutions to a class of Aronsson's equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changyou Wang, Juhana Siljander, Yuan Zhou","submitted_at":"2014-09-24T02:55:14Z","abstract_excerpt":"For any open set $\\Omega\\subset\\mathbb R^n$ and $n\\ge 2$, we establish everywhere differentiability of viscosity solutions to the Aronsson equation $$ <D_x(H(x, Du)), D_p H(x, Du)>=0 \\quad \\rm in\\ \\ \\Omega, $$ where $H$ is given by $$H(x,\\,p)=<A(x)p,p>=\\sum_{i,\\,j=1}^na^{ij}(x)p_i p_j,\\ x\\in\\Omega, \\ p\\in\\mathbb R^n, $$ and $A=(a^{ij}(x))\\in C^{1,1}(\\bar\\Omega,\\mathbb R^{n\\times n})$ is uniformly elliptic. This extends an earlier theorem by Evans and Smart \\cite{es11a} on infinity harmonic functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6804","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"}