Gradient estimate of a Dirichlet eigenfunction on a compact manifold with boundary

Yiqian Shi, Bin Xu

Let $e_{ł}(x)$ be an eigenfunction with respect to the Dirichlet Laplacian ${\Delta }_N$ on a compact Riemannian manifold $N$ with boundary: ${\Delta }_N{e}_{ł}={ł}^2{e}_{ł}$ in the interior of $N$ and $e_ł…