This book is a synthesis of recent advances in the spectral theory of the magnetic
Schrödinger operator. It can be considered a catalog of concrete examples of magnetic …

We consider the problem of minimizing or maximizing the quantity λ (Ω) T q (Ω) on the class
of open sets of prescribed Lebesgue measure. Here q> 0 is fixed, λ (Ω) denotes the first …

We consider the Laplacian on a class of smooth domains Ω⊂ R ν, ν≥ 2, with attractive
Robin boundary conditions: Q α Ω u=− Δ u,∂ u∂ n= α u on∂ Ω, α> 0, where n is the outer …

The plane waveguides with corners considered here are infinite V-shaped strips with
constant thickness. They are parametrized by their sole opening angle. We study the …

We consider the torsional rigidity and the principal eigenvalue related to the p-Laplace
operator. The goal is to find upper and lower bounds to products of suitable powers of the …

Assuming various points of view (power series expansions, Feshbach–Grushin reductions,
WKB constructions, coherent states decompositions, normal forms) a theory of Magnetic …

We study the localization effect for the eigenfunctions of the Laplace-Dirichlet problem in a
thin three-dimensional plate with curved non-smooth bases. We show that the …

We consider a spectral problem for the Laplacian operator in a planar T-like shaped thin
structure Ω ε, where ε denotes the transversal thickness of both branches. We assume the …

The authors consider the time-dependent Schrödinger equation on a Riemannian manifold
with a potential that localizes a certain subspace of states close to a fixed submanifold …

The simplest modeling of planar quantum waveguides is the Dirichlet eigenproblem for the
Laplace operator in unbounded open sets which are uniformly thin in one direction. Here we …