{"paper":{"title":"Boundary value problem and the Ehrhard inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Paata Ivanisvili","submitted_at":"2016-05-16T17:06:58Z","abstract_excerpt":"Let $I, J\\subset \\mathbb{R}$ be closed intervals, and let $H$ be $C^{3}$ smooth real valued function on $I\\times J$ with nonvanishing $H_{x}$ and $H_{y}$. Take any fixed positive numbers $a,b$, and let $d\\mu$ be a probability measure with finite moments and absolutely continuous with respect to Lebesgue measure. We show that for the inequality $$ \\int_{\\mathbb{R}^{n}} \\mathrm{ess\\,sup}_{y \\in \\mathbb{R}^{n}}\\; H\\left( f\\left(\\frac{x-y}{a}\\right),g\\left(\\frac{y}{b}\\right)\\right)d\\mu (x) \\geq H\\left(\\int_{\\mathbb{R}^{n}}fd\\mu, \\int_{\\mathbb{R}^{n}}gd\\mu \\right) $$ to hold for all Borel functions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04840","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"}