Asymptotic shape optimization for Riesz means of the Dirichlet Laplacian over convex domains

Simon Larson

For $\Omega \subset {\mathbb{R}}^n$, a convex and bounded domain, we study the spectrum of $-{\Delta }_{\Omega }$ the Dirichlet Laplacian on $\Omega$. For $\Lambda \ge 0$ and $\gamma \ge 0$ let ${\Omega }_{\Lambda ,\gamma }(\mathcal{A})$ den…