The Landis conjecture on exponential decay

• 成果类型: Article
• 署名作者: Logunov, A.; Malinnikova, E.; Nadirashvili, N.; Nazarov, F.
• 署名单位: Massachusetts Institute of Technology (MIT); Stanford University; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); University System of Ohio; Kent State University; Kent State University Kent; Kent State University Salem
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-025-01340-1
• 发表日期: 2025
• 页码: 465-508
• 关键词: quantitative uniqueness

摘要

Consider a solution u to Delta u + Vu = 0 on R-2, where V is real-valued, measurable and |V|<= 1. If |u(x)| <= exp (-C|x|log(1/2)|x|), |x| > 2, where C is a sufficiently large absolute constant, then u equivalent to 0.