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Pedro Caro

Publications and source records attributed to Pedro Caro.

28 records · Page 2Linked to original sources
arXiv2015

Stability of inverse problems in an infinite slab with partial data

In this paper, we study the stability of two inverse boundary value problems in an infinite slab with partial data. These problems have been studied by Li and Uhlmann for the case of the Schrodinger equation and by Krupchyk, Lassas and Uhlmann for the case of the magnetic Schrodinger equation. Here we quantify the method of uniqueness proposed by Li and Uhlmann and prove a log-log stability estimate for the inverse problems associated to the Schrodinger equation. The boundary measurements considered in these problems are modelled by partial knowledge of the Dirichlet-to-Neumann map: in the first inverse problem, the corresponding Dirichlet and Neumann data are known on different boundary hyperplanes of the slab; in the second inverse problem, they are known on the same boundary hyperplane of the slab.

math.AP↗
arXiv2014

Stability of the Calderón problem in admissible geometries

In this paper we prove log log type stability estimates for inverse boundary value problems on admissible Riemannian manifolds of dimension $n \geq 3$. The stability estimates correspond to a couple of uniqueness results by Dos Santos Ferrera, Kenig, Salo and Uhlmann. These inverse problems arise naturally when studying the anisotropic Calderón problem.

math.AP↗
arXiv2014

Stability estimates for the Calderón problem with partial data

This is a follow-up of a previous article where we proved local stability estimates for a potential in a Schrödinger equation on an open bounded set in dimension $n=3$ from the Dirichlet-to-Neumann map with partial data. The region under control was the penumbra delimited by a source of light outside of the convex hull of the open set. These local estimates provided stability of log-log type corresponding to the uniqueness results in Calderón's inverse problem with partial data proved by Kenig, Sjöstrand and Uhlmann. In this article, we prove the corresponding global estimates in all dimensions higher than three. The estimates are based on the construction of solutions of the Schrödinger equation by complex geometrical optics developed in the anisotropic setting by Dos Santos Ferreira, Kenig, Salo and Uhlmann to solve the Calderón problem in certain admissible geometries.

math.AP↗
arXiv2013

On global uniqueness for an IBVP for the time-harmonic Maxwell equations

In this paper we prove uniqueness for an inverse boundary value problem (IBVP) arising in electrodynamics. We assume that the electromagnetic properties of the medium, namely the magnetic permeability, the electric permittivity and the conductivity, are described by continuously differentiable functions.

math.AP↗
arXiv2012

Stability estimates for the Radon transform with restricted data and applications

In this article, we prove a stability estimate going from the Radon transform of a function with limited angle-distance data to the $L^p$ norm of the function itself, under some conditions on the support of the function. We apply this theorem to obtain stability estimates for an inverse boundary value problem with partial data.

math.AP↗
arXiv2009

Inverse boundary value problem for Maxwell equations with local data

We prove a uniqueness theorem for an inverse boundary value problem for the Maxwell system with boundary data assumed known only in part of the bound- ary. We assume that the inaccessible part of the boundary is either part of a plane, or part of a sphere. This work generalizes the results obtained by Isakov for the Schrödinger equation to Maxwell equations.

math.AP↗