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
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}.
