Year: 2026
Type: preprint
Abstract: We establish two complementary lower-bound mechanisms for individual eigenvalues of the Dirichlet Laplacian. First, energy orthogonality yields a frequency-dependent cap on the Fourier density of a finite spectral projection. Combining this cap with the standard $L^2$ Bessel estimate and a radial-capacity bathtub principle gives, on every open set of finite positive measure in $\mathbb R^n$ with $n\geq2$, \[ λ_k\geq c_n(2π)^2ω_n^{-2/n}|Ω|^{-2/n}k^{2/n}, \qquad \frac{n}{n+2}
Source: arXiv (Cornell University)
Authors: Wang, Yifan, Xie, Hehu
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213422964