Failure of strong unique continuation for harmonic functions on RCD spaces

被引：0
|
作者：
Deng, Qin [1 ]
Zhao, Xinrui [1 ]
机构：
[1] MIT, Dept Math, 77 Massachusetts Ave, Cambridge, MA 02139 USA
来源：
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2023年 / 2023卷 / 795期
基金：
美国国家科学基金会;
关键词：
METRIC-MEASURE-SPACES; RICCI CURVATURE; ELLIPTIC-EQUATIONS; DIVERGENCE FORM; LAPLACIAN;
D O I：
10.1515/crelle-2022-0090
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Unique continuation of harmonic functions on RCD space is a long-standing open problem, with little known even in the setting of Alexandrov spaces. In this paper, we establish the weak unique continuation theorem for harmonic functions on RCD(K, 2) spaces and give a counterexample for strong unique continuation in the setting of RCD(K, N) space for any N >= 4 and any K is an element of R.
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页码：221 / 241
页数：21
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