In this work we consider the two-dimensional Dirac operator with general local singular
interactions supported on a closed curve. A systematic study of the interaction is performed …

We prove Strichartz estimates for the Schrödinger equation with an electromagnetic
potential, in dimension n⩾ 3. The decay and regularity assumptions on the potentials are …

This paper deals with global dispersive properties of Schrödinger equations with real-valued
potentials exhibiting critical singularities, where our class of potentials is more general than …

The purpose of this paper is to study the validity of global-in-time Strichartz estimates for the
Schrödinger equation on R n, n≥ 3, with the negative inverse-square potential− σ| x|− 2 in …

We analyze the dispersive properties of a Dirac system perturbed with a magnetic field. We
prove a general virial identity; as applications, we obtain smoothing and endpoint Strichartz …

The Gross-Pitaevskii equation, or more generally the nonlinear Schrödinger equation,
models the Bose-Einstein condensates in a macroscopic gaseous superfluid wave-matter …

We study the forward problem of the magnetic Schrödinger operator with potentials that
have a strong singularity at the origin. We obtain new resolvent estimates and give some …

We quantify the subcriticality of the bilaplacian in dimensions greater than four by providing
explicit repulsivity/smallness conditions on complex additive perturbations under which the …

Several recent papers have focused their attention in proving the correct analogue to the
Lieb-Thirring inequalities for non self-adjoint operators and in finding bounds on the …

We study the electromagnetic Helmholtz equation with the magnetic vector potential b (x)
and n (x) a variable index of refraction that does not necessarily converge to a constant at …