{"paper":{"title":"Optimal Hardy inequalities in cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"Baptiste Devyver, Georgios Psaradakis, Yehuda Pinchover","submitted_at":"2015-02-18T12:53:54Z","abstract_excerpt":"Let $\\Omega$ be an open connected cone in $\\mathbb{R}^n$ with vertex at the origin. Assume that the operator $$P_\\mu:=-\\Delta-\\frac{\\mu}{\\delta_\\Omega^2(x)}$$ is {\\em subcritical} in $\\Omega$, where $\\delta_\\Omega$ is the distance function to the boundary of $\\Omega$ and $\\mu \\leq 1/4$. We show that under some smoothness assumption on $\\Omega$, the following improved Hardy-type inequality \\begin{equation*}\n  \\int_{\\Omega}|\\nabla \\varphi|^2\\,\\mathrm{d}x -\\mu\\int_{\\Omega} \\frac{|\\varphi|^2}{\\delta_\\Omega^2}\\,\\mathrm{d}x \\geq \\lambda(\\mu)\\int_{\\Omega} \\frac{|\\varphi|^2}{|x|^2}\\,\\mathrm{d}x \\qquad"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05205","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"}