{"paper":{"title":"Two classical properties of the Bessel quotient $I_{\\nu+1}/I_\\nu$ and their implications in pde's","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nicola Garofalo","submitted_at":"2018-10-23T10:15:11Z","abstract_excerpt":"Two elementary and classical results about the Bessel quotient $y_\\nu = \\frac{I_{\\nu+1}}{I_\\nu}$ state that on the half-line $(0,\\infty)$ one has for $\\nu\\ge -1/2$: \\begin{itemize} \\item[(i)] $0 < y_\\nu< 1$; \\item[(ii)] $y_\\nu$ is strictly increasing. \\end{itemize} In this paper we show that (i) and (ii) have some nontrivial and interesting applications to pde's. As a consequence of them, we establish some sharp new results for a class of degenerate partial differential equations of parabolic type in $\\Rnp\\times (0,\\infty)$ which arise in connection with the analysis of the fractional heat ope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09756","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"}