论文标题
关于Dirichlet Laplacian的两项Weyl公式的误差
On the error in the two-term Weyl formula for the Dirichlet Laplacian
论文作者
论文摘要
我们研究了Lipschitz的常规子集的$ \ Mathbb {r}^d $的常规子集中的Dirichlet Laplacian的两项Weyl定律中其余术语的最佳性。特别是，对于热核痕迹的短期渐近造型，我们证明，错误术语不能比第二学期的小$ o $更好地使误差术语更好。
We study the optimality of the remainder term in the two-term Weyl law for the Dirichlet Laplacian within the class of Lipschitz regular subsets of $\mathbb{R}^d$. In particular, for the short-time asymptotics of the trace of the heat kernel we prove that the error term cannot be made quantitatively better than little-$o$ of the second term.
