{"paper":{"title":"Intrinsic Geometry and Analysis of Diffusion Processes and $L^\\infty$-Variational Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA","math.PR"],"primary_cat":"math.CA","authors_text":"Nageswari Shanmugalingam, Pekka Koskela, Yuan Zhou","submitted_at":"2013-05-27T07:32:34Z","abstract_excerpt":"The aim of this paper is two-fold:\n  First, we obtain a better understanding of the intrinsic distance of diffusion processes. Precisely, (i) for all $n\\ge1$, the diffusion matrix $A$ is weak upper semicontinuous on $\\Omega$ if and only if the intrinsic differential and the local intrinsic distance structures coincide; (ii) if $n=1$, or if $n\\ge2$ and $A$ is weak upper semicontinuous on $\\Omega$, the intrinsic distance and differential structures always coincide; (iii) if $n\\ge2$ and $A$ fails to be weak upper semicontinuous on $\\Omega$, the (non-) coincidence of the intrinsic distance and dif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6130","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"}