Upper and lower bounds for normal derivatives of spectral clusters of Dirichlet Laplacian

Xiangjin Xu

In this paper, we prove the upper and lower bounds for normal derivatives of spectral clusters $u={\chi }_{\lambda }^{s}f$ of Dirichlet Laplacian ${\Delta }_M$, $$c_s λ\|u\|_{L^2(M)} \leq \| \partial_νu \…