Perturbation of eigenvalues due to gaps in two-dimensional boundaries
Perturbation of eigenvalues due to gaps in two-dimensional boundaries
Motivated by problems involving diffusion through small gaps, we revisit two-dimensional eigenvalue problems with localized perturbations to Neumann boundary conditions. We recover the known result that the gravest eigenvalue is O (|ln ϵ | −1 ), where ϵ is the ratio of the size of the hole to the length-scale …