{"paper":{"title":"The Landis Conjecture for variable coefficient second-order elliptic PDES","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Blair Davey, Carlos Kenig, Jenn-Nan Wang","submitted_at":"2015-10-16T02:26:38Z","abstract_excerpt":"In this work, we study the Landis conjecture for second-order elliptic equations in the plane. Precisely, assume that $V\\ge 0$ is a measurable real-valued function satisfying $\\|V\\|_{L^\\infty({\\mathbb R}^2)} \\le 1$. Let $u$ be a real solution to $\\mbox{div}(A \\nabla u) - V u = 0$ in ${\\mathbb R}^2$. Assume that $|u(z)| \\le \\exp(c_0 |z|)$ and $u(0) = 1$. Then, for any $R$ sufficiently large, \\[ \\inf_{|z_0| = R} \\|u\\|_{L^\\infty(B_1(z_0))} \\ge \\exp(- C R \\log R). \\] In addition to equations with electric potentials, we also derive similar estimates for equations with magnetic potentials. The proo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04762","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"}