Unique Continuation at the Boundary for Harmonic Functions in C1 Domains and Lipschitz Domains with Small Constant
Unique Continuation at the Boundary for Harmonic Functions in C1 Domains and Lipschitz Domains with Small Constant
复制标题
小常数C1域和Lipschitz域调和函数边界的唯一延拓
DOI：
--
复制
发表时间：
2020
影响因子：
3
通讯作者：
X. Tolsa
中科院分区：
文献类型：
--
作者：
X. Tolsa
设Ω n是一个C1整环，或更一般地，一个局部Lipschitz常数较小的Lipschitz整环。本文证明了：如果u是Ω中的调和函数且在Ω Ω中为零，且u的法导数在∑的具有正表面测度的子集中为零，则u恒为零.版权所有© 2021作者。纯数学与应用数学通讯（Communications on Pure and Applied Mathematics），Wiley Periodicals LLC出版。
Let Ω⊂ℝn be a C1 domain, or more generally, a Lipschitz domain with small local Lipschitz constant. In this paper it is shown that if u is a function harmonic in Ω and continuous in Ω¯ , which vanishes in a relatively open subset ∑⊂∂Ω ; moreover, the normal derivative ∂νu vanishes in a subset of ∑ with positive surface measure; then u is identically zero. © 2021 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.
$$C^1$$-Dini域上的边界唯一延拓和奇异集的大小
影响因子：
2.5
作者：
Kenig, Carlos;Zhao, Zihui
通讯作者：
Zhao, Zihui