论文标题
在$ c^1 $域和Lipschitz域中的谐波功能的边界的独特延续
Unique continuation at the boundary for harmonic functions in $C^1$ domains and Lipschitz domains with small constant
论文作者
论文摘要
令$ω\ subset \ mathbb r^n $为$ c^1 $域，或更一般的lipschitz域，带有小的本地Lipschitz常数。在本文中，表明，如果$ u $是$ω$的函数谐音，并且连续$ \叠加ω$在相对开放的子集$σ\ subset \partialΩ$中消失，此外，正常的衍生衍生物$ \partial_νu$ $ $ $ $ u $ $ $ $ $ $ 0。
Let $Ω\subset\mathbb R^n$ be a $C^1$ 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 $\overline Ω$ which vanishes in a relatively open subset $Σ\subset\partialΩ$ and moreover the normal derivative $\partial_νu$ vanishes in a subset of $Σ$ with positive surface measure, then $u$ is identically $0$.
