{"paper":{"title":"Differentiability of the argmin function and a minimum principle for semiconcave subsolutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"David Witt Nystr\\\"om, Julius Ross","submitted_at":"2018-08-13T18:51:49Z","abstract_excerpt":"Suppose $f(x,y) + \\frac{\\kappa}{2} \\|x\\|^2 - \\frac{\\sigma}{2}\\|y\\|^2$ is convex where $\\sigma>0$, and the argmin function $\\gamma(x) = \\{ \\gamma : \\inf_y f(x,y) = f(x,\\gamma)\\}$ exists and is single valued. We will prove $\\gamma$ is differentiable almost everywhere. As an application we deduce a minimum principle for certain semiconcave subsolutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04402","kind":"arxiv","version":2},"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"}