arXiv subjects

Andoni García

Publications and source records attributed to Andoni García.

5 recordsLinked to original sources

arXiv2015

Discreteness of Transmission Eigenvalues for Higher-Order Main Terms and Perturbations

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-order perturbations. The coefficients of the perturbations must be sufficiently smooth and the coefficients of the higher-order terms of the perturbation must vanish in a neighbourhood of the boundary of the underlying domain. The zeroeth order term must satisfy a suitable coercivity condition in a neighbourhood of the boundary.

math.SP↗

arXiv2013

$L^p$-$L^q$ estimates for Electromagnetic Helmholtz equation. Singular potentials

In space dimension $n\geq3$, we consider the electromagnetic Schrödinger Hamiltonian $H=(\nabla-iA(x))^2+V$ and the corresponding Helmholtz equation (\nabla-iA(x))^2u+u+V(x)u=f\quad \text{in}\quad \mathbb{R}^n, where the magnetic and electric potentials are allowed to have singularities at the origin and decay at infinity. We extend the well known $L^p$-$L^q$ estimates for the solution of the free Helmholtz equation to the case when the electromagnetic hamiltonian $H$ is considered. This work extends the results that appear in \cite{G}.

math.AP↗

arXiv2013

Reconstruction from boundary measurements for less regular conductivities

In this paper, following Nachman's idea and Haberman and Tataru's idea, we reconstruct $C^1$ conductivity $γ$ or Lipchitz conductivity $γ$ with small enough value of $|\nabla logγ|$ in a Lipschitz domain $Ω$ from the Dirichlet-to-Neumann map $Λ_γ$. In the appendix the authors and R. M. Brown recover the gradient of a $C^1$-conductivity at the boundary of a Lipschitz domain from the Dirichlet-to-Neumann map $Λ_γ$.

math.AP↗

arXiv2012

Stability of the Calderón problem for less regular conductivities

In these notes we prove log-type stability for the Calderón problem with conductivities in $ C^{1,\varepsilon}(\barΩ) $. We follow the lines of a recent work by Haberman and Tataru in which they prove uniqueness for $ C^1(\barΩ) $.

math.AP↗

arXiv2011

On the lack of dispersion for a class of magnetic Dirac flows

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 some explicit examples of homogeneous magnetic potentials with less than Coulomb decay, i. e. with homogeneity-degree more than -1, such that the magnetic field points to a fixed direction, which does not depend on $x\in \mathbb{R}^3$.

math.AP↗