{"paper":{"title":"A class of weighted Hardy inequalities and applications to evolution problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anna Canale, Ciro Tarantino, Francesco Pappalardo","submitted_at":"2018-12-07T19:34:29Z","abstract_excerpt":"\\begin{abstract} We state the following weighted Hardy inequality \\begin{equation*} c_{o, \\mu}\\int_{{\\R}^N}\\frac{\\varphi^2 }{|x|^2}\\, d\\mu\\le \\int_{{\\R}^N} |\\nabla\\varphi|^2 \\, d\\mu +\n  K \\int_{\\R^N}\\varphi^2 \\, d\\mu \\quad \\forall\\, \\varphi \\in H_\\mu^1 %\\qquad c\\le c_\\mu, \\end{equation*} in the context of the study of the Kolmogorov operators \\begin{equation*} Lu=\\Delta u+\\frac{\\nabla \\mu}{\\mu}\\cdot\\nabla u \\end{equation*} perturbed by inverse square potentials and of the related evolution problems. The function $\\mu$ in the drift term is a probability density on $\\R^N$. We prove the optimalit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03193","kind":"arxiv","version":3},"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"}