{"paper":{"title":"A Meshkov-type construction for the borderline case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Blair Davey","submitted_at":"2014-03-29T00:23:20Z","abstract_excerpt":"We construct functions $u: \\mathbb{R}^2 \\to \\mathbb{C}$ that satisfy an elliptic eigenvalue equation of the form $-\\Delta u + W \\cdot \\nabla u + V u = \\lambda u$, where $\\lambda \\in \\mathbb{C}$, and $V$ and $W$ satisfy $|V(x)| \\lesssim <x>^{-N}$, and $|W(x)| \\lesssim <x>^{-P}$, with $\\min\\{N, P\\} = 1/2$. For $|x|$ sufficiently large, these solutions satisfy $|u(x)| \\lesssim \\exp(- c|x|)$. In the author's previous work, examples of solutions over $\\mathbb{R}^2$ were constructed for all $N, P$ such that $\\min\\{N,P\\} \\in [0, 1/2)$. These solutions were shown to have the optimal rate of decay at i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7572","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"}