论文标题
关于具有分数模量的半号函数的扩展问题
On the extension problem for semiconcave functions with fractional modulus
论文作者
论文摘要
考虑一个本地Lipschitz函数$ u $ u $在可能无限的开放子集$ω$ of $ \ mathbb {r}^n $带有$ c^{1,1} $边界的闭合。假设$ u $是$ \ overlineω$的semiconcave，其分数半腔模量。是否可以在任何边界点保持相同半腔模量的社区中扩展$ u $？我们表明确实如此，我们给出了此扩展属性的两个应用程序。首先，我们得出了在封闭域上函数的近似结果。然后，我们使用上述扩展特性来研究边界点半循环函数的奇异性的传播。
Consider a locally Lipschitz function $u$ on the closure of a possibly unbounded open subset $Ω$ of $\mathbb{R}^n$ with $C^{1,1}$ boundary. Suppose $u$ is semiconcave on $\overline Ω$ with a fractional semiconcavity modulus. Is it possible to extend $u$ in a neighborhood of any boundary point retaining the same semiconcavity modulus? We show that this is indeed the case and we give two applications of this extension property. First, we derive an approximation result for semiconcave functions on closed domains. Then, we use the above extension property to study the propagation of singularities of semiconcave functions at boundary points.
