{"paper":{"title":"On the Strong unique continuation property of a degenerate elliptic operator with Hardy type potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Agnid Banerjee, Arka Mallick","submitted_at":"2018-07-05T11:41:09Z","abstract_excerpt":"In this paper we prove strong unique continuation for the following degenerate elliptic equation \\begin{equation}\\label{e0} \\Delta_zu +|z|^2\\partial_t^2u = Vu,\\quad (z,t) \\in \\mathbb{R}^N \\times \\mathbb{R} \\end{equation} where the potential $V$ satisfies either of the following growth assumptions \\begin{align} & |V(z,t)| \\leq \\frac{f(\\rho(z,t))}{\\rho(z,t)^2},\\ \\text{where $f$ satisfies the Dini integrability condition as in (1.3)} \\\\ & \\text{or when } \\notag \\\\ & |V(z,t)| \\leq C\\frac{\\psi(z,t)^{\\epsilon}}{\\rho(z,t)^2},\\ \\text{for some $\\epsilon>0$ with $\\psi$ as in (2.6) and $N$ even.} \\notag "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01947","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"}