论文标题

C1,1开放式α稳定过程的光谱热含量

Spectral heat content for α-stable processes in C1,1 open sets

论文作者

Park, Hyunchul, Song, Renming

论文摘要

在本文中,我们研究了光谱热内容的$ t \ downarrow 0 $,$ q^{(α)} _ {d}(d}(t)$用于同变性$α$ - 稳定过程,$α\ $ c^in [1,2)$ in In In In bounded $ C^{1,1,1,1,1,1,1,1,1 $ c} $ d \ geq 2 $。以及\ cit {val2017}的结果,$ d = 1 $和\ cite {gps19}对于$α\(0,1)$中的$α\,本文的主要定理建立了光谱热量的渐近行为,直到第二个期限为$α\ in(0,2)$ in(0,2)$ d \ geq1 $ d \ geq1,并在($ de)中的第二学期均建立。 \ cite {val2017}。

In this paper we study the asymptotic behavior, as $t\downarrow 0$, of the spectral heat content $Q^{(α)}_{D}(t)$ for isotropic $α$-stable processes, $α\in [1,2)$, in bounded $C^{1,1}$ open sets $D\subset \R^{d}$, $d\geq 2$. Together with the results from \cite{Val2017} for $d=1$ and \cite{GPS19} for $α\in (0,1)$, the main theorem of this paper establishes the asymptotic behavior of the spectral heat content up to the second term for all $α\in (0,2)$ and $d\geq1$, and resolves the conjecture raised in \cite{Val2017}.

扫码加入交流群

加入微信交流群

微信交流群二维码

扫码加入学术交流群,获取更多资源