Juan Antonio Barceló

Weak Dispersive Estimates for Schrödinger Equations with Long Range Potentials

We prove local smoothing estimates for the Schrödinger initial value problem with data in the energy space L 2(ℝ d ), d ≥ 2 and a general class of potentials. In the repulsive setting we have to assume just a power like decay (1 + |x|)−γ for some γ > 0. Also attractive perturbations are considered. The estimates hold for all time and as a consequence a weak dispersion of the solution is obtained. The proofs are based on similar estimates for the corresponding stationary Helmholtz equation and Kato H-smooth theory.

Strichartz inequalities with weights in Morrey-Campanato classes

We prove some weighted refinements of the classical Strichartz inequalities for initial data in the Sobolev spaces Ḣs(ℝn). We control the weightedL2-norm of the solution of the free Schrödinger equation whenever the weight is in a Morrey-Campanato type space adapted to that equation. Our partial positive results are complemented by some necessary conditions based on estimates for certain particular solutions of the free Schrödinger equation.

RECONSTRUCTION OF DISCONTINUITIES FROM BACKSCATTERING DATA IN TWO DIMENSIONS

We prove that the nonsmooth part of a noncompactly supported potential

A Multilinear Extension Inequality In Rn

q

A bilinear extension inequality in two dimensions

in the Schrodinger Hamiltonian

Numerical approximation of the potential in the two-dimesional inverse scattering problem

-\Delta+q

Resolvent and Strichartz estimates for elastic wave equations

, in dimension

A Born Approximation for Live Loads in Navier Elasticity

n=2

A MULTILINEAR EXTENSION INEQUALITY IN

, is contained in its Born approximation

\mathbb{R}^{n}

q_B