5 problems

Let $\Omega\subset\mathbb{R}^d$ be any bounded set, and let the magnetic field be constant. Denote by $\lambda^{\rm DN}(A,\Omega)$ the ground-state energy of the magnetic Dirichlet…

Let $\Omega$ be a regular domain in $\mathbb{R}^2$, let $A_0$ be a magnetic potential whose magnetic field is constant and has norm $1$, and let $\lambda^{\rm DN}(bA_0,\Omega)$ den…

Let $\Omega$ be a regular domain in $\mathbb{R}^2$, and let $A_0$ be a magnetic potential whose magnetic field is constant and has norm $1$. Let $\Lambda_{bA_0}$ be the associated…

Let $M$ be a Riemannian manifold with a boundary that need not be compact. The Dirichlet-to-Neumann operator and the associated mass-dependent quantities are as in Assumption … hol…

Let $\Lambda$ be the Dirichlet-to-Neumann operator, let $P_\tau$ denote the spectral projection associated with the threshold $\tau$, and let $J$ be the operator mapping $v$ to…