Magnetic confinement for the 3D Robin Laplacian

We determine accurate asymptotics of the lowest eigenvalue for the Laplace operator with a smooth magnetic field and Robin boundary conditions in a smooth 3D domain, when the Robin parameter tends to $+\mathrm{\infty }$. Our results identify a critical regime where the contribution of the magnetic field and the Robin condition are of the same order. In this critical regime, we derive an effective operator defined on the boundary of the domain.