论文标题
关于分数无穷laplacian的渐近扩展
On asymptotic expansions for the fractional infinity Laplacian
论文作者
论文摘要
在分数$ \ infty $ -laplacian $Δ_\ unfty^s $ for $ s \ in（\ frac {1} {1} {2} {2}，1）$的情况下，我们提出了两个相互关联的积分平均值的两个渐近扩展。该操作员已在[Bjorland，C.，Caffarelli，L。和Figalli，A.，\ textsl {非局部拖船 - 战线和非属性分数laplacian}，Comm。纯应用。数学，\ textbf {65}，第337--380页，（2012）]。我们的扩展是由删除的奇异性$ε$的半径进行参数的，并允许识别$δ_\ infty^sx（x）$作为$ε^{2S} $ - $ε$ - $ε$ - aververy valueververal value $ $ $ ϕ（x）$的偏差的订单系数，y limit unip $ nimim $ $。平均值适合仅是borel常规且有限的功能$ ϕ $。
We propose two asymptotic expansions of two interrelated integral-type averages, in the context of the fractional $\infty$-Laplacian $Δ_\infty^s$ for $s\in (\frac{1}{2},1)$. This operator has been introduced and first studied in [Bjorland, C., Caffarelli, L. and Figalli, A., \textsl{Nonlocal Tug-of-War and the inifnity fractional Laplacian}, Comm. Pure Appl. Math., \textbf{65}, pp. 337--380, (2012)]. Our expansions are parametrised by the radius of the removed singularity $ε$, and allow for the identification of $Δ_\infty^sϕ(x)$ as the $ε^{2s}$-order coefficient of the deviation of the $ε$-average from the value $ϕ(x)$, in the limit $ε\to 0+$. The averages are well posed for functions $ϕ$ that are only Borel regular and bounded.
