Search results for " calderón"
showing 4 items of 14 documents
Quantitative Approximation Properties for the Fractional Heat Equation
2017
In this note we analyse \emph{quantitative} approximation properties of a certain class of \emph{nonlocal} equations: Viewing the fractional heat equation as a model problem, which involves both \emph{local} and \emph{nonlocal} pseudodifferential operators, we study quantitative approximation properties of solutions to it. First, relying on Runge type arguments, we give an alternative proof of certain \emph{qualitative} approximation results from \cite{DSV16}. Using propagation of smallness arguments, we then provide bounds on the \emph{cost} of approximate controllability and thus quantify the approximation properties of solutions to the fractional heat equation. Finally, we discuss genera…
The higher order fractional Calderón problem for linear local operators : Uniqueness
2020
We study an inverse problem for the fractional Schr\"odinger equation (FSE) with a local perturbation by a linear partial differential operator (PDO) of order smaller than the order of the fractional Laplacian. We show that one can uniquely recover the coefficients of the PDO from the Dirichlet-to-Neumann (DN) map associated to the perturbed FSE. This is proved for two classes of coefficients: coefficients which belong to certain spaces of Sobolev multipliers and coefficients which belong to fractional Sobolev spaces with bounded derivatives. Our study generalizes recent results for the zeroth and first order perturbations to higher order perturbations.
On some partial data Calderón type problems with mixed boundary conditions
2021
In this article we consider the simultaneous recovery of bulk and boundary potentials in (degenerate) elliptic equations modelling (degenerate) conducting media with inaccessible boundaries. This connects local and nonlocal Calderón type problems. We prove two main results on these type of problems: On the one hand, we derive simultaneous bulk and boundary Runge approximation results. Building on these, we deduce uniqueness for localized bulk and boundary potentials. On the other hand, we construct a family of CGO solutions associated with the corresponding equations. These allow us to deduce uniqueness results for arbitrary bounded, not necessarily localized bulk and boundary potentials. T…
El Maestrazgo del Tusón, de Pedro Calderón de la Barca: la dramaturgia de un mito histórico. Estudio y edición crítica
2014
La presente tesis doctoral aborda la consideración del auto calderoniano "El Maestrazgo del Tusón" (1659) en su doble vertiente de texto literario y texto espectacular, facetas inseparables en el análisis de todo texto dramático. El trabajo se ha estructurado en dos partes, de acuerdo con los objetivos perseguidos. En primera instancia, el propósito ha sido el de ofrecer –siguiendo los principios de la crítica textual moderna– una edición crítica fiable de uno de los autos que Pedro Calderón de la Barca (1600-1681) compuso en su época de plenitud dramática: "El Maestrazgo del Tusón", una pieza que, hasta la fecha, carecía de una fijación textual definitiva. El texto del auto se ha acompañad…