Small-scale mass estimates for Neumann eigenfunctions: piecewise smooth planar domains

Hans Christianson, John A. Toth

Let $\Omega$ be a piecewise-smooth, bounded convex domain in ${\mathbb{R}}^2$ and consider $L^2$-normalized Neumann eigenfunctions ${\varphi }_{\lambda }$ with eigenvalue ${\lambda }^2$. Our main result is a small-scale {\…