{"paper":{"title":"Landis' conjecture for general second order elliptic equations with singular lower order terms in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Blair Davey, Jenn-Nan Wang","submitted_at":"2017-09-26T14:29:56Z","abstract_excerpt":"In this article, we study the order of vanishing and a quantitative form of Landis' conjecture in the plane for solutions to second-order elliptic equations with variable coefficients and singular lower order terms. Precisely, we let $A$ be real-valued, bounded and elliptic, but not necessary symmetric or continuous, and we assume that $V$ and $W_i$ are real-valued and belong to $L^p$ and $L^{q_i}$, respectively. We prove that if $u$ is a real-valued, bounded and normalized solution to an equation of the form $-\\nabla \\cdot (A \\nabla u + W_1 u) + W_2 \\cdot \\nabla u + V u = 0$ in $B_d$, then un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09042","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"}