The Weyl-law conjecture for Love waves in layered elastic half-spaces

Let $n\geqslant3$, let $y\in[1/C_\infty,1/C_0)$, and let $\widetilde{C}_1\leqslant\cdots\leqslant\widetilde{C}_{n+1}$ be the nondecreasing reordering of the parameters $C_1,\ldots,C_{n+1}$, with associated sequences $\tilde{\nu}_p$ and $\widetilde{T}_p$. Let $N(\omega,y)$ denote the counting function for the Love-wave problem. Weyl-law conjecture. As $\omega$ goes to $+\infty$, one has

$$N(\omega,y)\sim\frac{\omega}{\pi}\sum_{p=1}^{j}|\tilde{\nu}_p(y)|\widetilde{T}_p,$$

if $y\in[1/\widetilde{C}_{j+1},1/\widetilde{C}_j)$. This conjecture extends the proved asymptotic formula to the whole interval $[1/C_\infty,1/C_0)$ without assuming $C_0<\widetilde{C}_2$, thereby allowing several of the $C_j$ to equal $C_0:=\min_j C_j$.