This book is the second edition of the book Lectures on nonlinear evolution equations. Initial
value problems [150] from 1992. Additionally, it now includes a new Chapter 13 on initial …

We show a family of virial-type identities for the Schrödinger and wave equations with
electromagnetic potentials. As a consequence, some weak dispersive inequalities in space …

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 …

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 prove a local in time smoothing estimate for a magnetic Schrödinger equation with
coefficients growing polynomially at spatial infinity. The assumptions on the magnetic field …

We prove smoothing estimates in Morrey--Campanato spaces for a Helmholtz equation -
Lu+zu=f, -Lu:=∇^b(a(x)∇^bu)-c(x)u, ∇^b:=∇+ib(x) with fully variable coefficients, of limited …

We study the Helmholtz equationin ℝd with magnetic and electric potentials that are singular
at the origin and decay at∞. We prove the existence of a unique solution satisfying a …

We study the Helmholtz equation with electromagnetic-type perturbations, in the exterior of a
domain, in dimension n≥ 3. Using multiplier techniques in the style of Morawetz, we prove a …

In this paper we develop the classical multiplier technique to build up a virial identity for the
electromagnetic variable coefficients Schrödinger equation. Following the strategy of …

El objetivo principal de esta tesis es estudiar el problema directo de la ecuación de
Helmholtz con potenciales eléctrico y magnético. Consideramos potenciales que permiten …