2 problems

Let $B$ denote the ball in $\mathbb{R}^3$, and let $\lambda_1(\Omega)$ be the first Maxwell eigenvalue of a domain $\Omega$. Consider domains subject to either a fixed-volume constrai…

Let $B$ denote the ball in $\mathbb{R}^3$, and let the first three Maxwell eigenvalues of a domain $\Omega$ be $\lambda_1(\Omega),\lambda_2(\Omega),\lambda_3(\Omega)$. For $j=1,2,3$, let…