11 citations · 19 across the 6 of their papers we have counts for
7 papers
Scattering with critically-singular and -shell potentials
Pedro Caro, Andoni Garcia
The authors consider a scattering problem for electric potentials that have a component which is critically singular in the sense of Lebesgue spaces, and a component given by a mea…
The Calderón problem with corrupted data
Pedro Caro, Andoni Garcia
We consider the inverse Calderón problem consisting of determining the conductivity inside a medium by electrical measurements on its surface. Ideally, these measurements determine…
Discreteness of Transmission Eigenvalues for Higher-Order Main Terms and Perturbations
Andoni García, Esa V. Vesalainen, Miren Zubeldia
In this paper we extend Sylvester's approach via upper triangular compact operators to establish the discreteness of transmission eigenvalues for higher-order main terms and higher…
On the lack of dispersion for a class of magnetic Dirac flows
Naiara Arrizabalaga, Luca Fanelli, Andoni García
We show that global Strichartz estimates for magnetic Dirac operators generally fails, if the potentials do not decay fast enough at infinity. In order to prove this, we construct…
Magnetic Virial and applications to blow up for Schrödinger and wave equations
Andoni Garcia
We prove blow up results for the solution of the initial value problem with negative energy of the focusing mass-critical and supercritical nonlinear Schrödinger and the focusing e…
- estimates for Electromagnetic Helmholtz equation
Andoni Garcia
In space dimension , we consider the electromagnetic Schrödinger Hamiltonian and the corresponding Helmholtz equation $(\nabla-iA(x))^2u+u-V(x)u=f \i…
Counterexamples to Strichartz estimates for the magnetic Schroedinger equation
Luca Fanelli, Andoni Garcia
In space dimension , we consider the magnetic Schrödinger Hamiltonian and the corresponding Schrödinger equation i\partial_tu+Hu=0. We show some expli…