论文标题
在嵌入分数阶的嵌入定理中的极端函数的稳定性上
On the constancy of the extremal function in the embedding theorem of fractional order
论文作者
论文摘要
我们考虑在界面lipschitz域$ω的分数嵌入定理$ \ mathcal {h}^s（ω）\ jookrightArrow l_q（ω）$中的最小化稳定性问题的问题，具体取决于域的大小。对于域$ \ varepsilonω的家族，$我们证明，对于小扩张系数$ \ varepsilon $，独特的最小化器是恒定的，而对于大$ \ varepsilon $，恒定功能甚至都不是本地最小化器。我们还讨论如果局部函数是局部函数，是否是全局最小化器。
We consider the problem of the minimizer constancy in the fractional embedding theorem $\mathcal{H}^s(Ω) \hookrightarrow L_q(Ω)$ for a bounded Lipschitz domain $Ω,$ depending on the domain size. For the family of domains $\varepsilon Ω,$ we prove that for small dilation coefficients $\varepsilon$ a unique minimizer is constant, whereas for large $\varepsilon$ a constant function is not even a local minimizer. We also discuss whether a constant function is a global minimizer if it is a local one.
