Boundary Unique Continuation on $$C^1$$-Dini Domains and the Size of the Singular Set
Boundary Unique Continuation on $$C^1$$-Dini Domains and the Size of the Singular Set
复制标题
$$C^1$$-Dini域上的边界唯一延拓和奇异集的大小
DOI：
10.1007/s00205-022-01771-7
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发表时间：
2022
影响因子：
2.5
通讯作者：
Zhao, Zihui
中科院分区：
文献类型：
--
作者：
Kenig, Carlos;Zhao, Zihui
设a-Dini域上的调和函数在边界面球上为零。我们考虑了它的一个有效形式的奇异集(直到边界)，并给出了它的高维Minkowski含量的估计，它只依赖于中心在0的某些修正的频率函数的上界。当标准频率函数在每个点都是单调的时，这样的结果在凸域的内部和边界上都是已知的。我们在Dini域上的工作的新奇之处在于如何补偿边界和内点上单调量的缺乏。
Letube a harmonic function in a-Dini domainsuch thatuvanishes on a boundary surface ball. We consider an effective version of its singular set (up to boundary)and give an estimate of its-dimensional Minkowski content, which only depends on the upper bound of some modified frequency function ofucentered at 0. Such results are already known in the interior and at the boundary of convex domains, when the standard frequency function is monotone at every point. The novelty of our work on Dini domains is how to compensate for the lack of such monotone quantities at boundary as well as interior points.
影响因子：
2.2
作者：
E. Schmidt;N. Weck
通讯作者：
E. Schmidt;N. Weck
影响因子：
4.9
作者：
J. Cheeger;A. Naber
通讯作者：
J. Cheeger;A. Naber