Browsing by Author "Ponce Vanegas, F."
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A Bilinear Strategy for Calderón's Problem
Ponce Vanegas, F. (201908)Electrical Impedance Imaging would suffer a serious obstruction if for two different conductivities the potential and current measured at the boundary were the same. The Calder\'on's problem is to decide whether the ... 
A Bilinear Strategy for Calderón’s Problem
Ponce Vanegas, F. (202005)Electrical Impedance Imaging would suffer a serious obstruction if two different conductivities yielded the same measurements of potential and current at the boundary. The Calderón’s problem is to decide whether the ... 
Convergence over fractals for the Schrödinger equation
Lucà, R.; Ponce Vanegas, F. (202101)We consider a fractal refinement of the Carleson problem for the Schrödinger equation, that is to identify the minimal regularity needed by the solutions to converge pointwise to their initial data almost everywhere with ... 
Counterexamples for the fractal Schrödinger convergence problem with an Intermediate Space Trick
Eceizabarrena, D.; Ponce Vanegas, F. (20211209)We construct counterexamples for the fractal Schrödinger convergence problem by combining a fractal extension of Bourgain's counterexample and the intermediate space trick of DuKimWangZhang. We confirm that the same ... 
The Frisch–Parisi formalism for fluctuations of the Schrödinger equation
Kumar, S.; Ponce Vanegas, F.; Roncal, L.; Vega, L. (2022)We consider the solution of the Schrödinger equation $u$ in $\mathbb{R}$ when the initial datum tends to the Dirac comb. Let $h_{\text{p}, \delta}(t)$ be the fluctuations in time of $\int\lvert x \rvert^{2\delta}\lvert ... 
Pointwise Convergence over Fractals for Dispersive Equations with Homogeneous Symbol
Eceizabarrena, D.; Ponce Vanegas, F. (20210824)We study the problem of pointwise convergence for equations of the type $i\hbar\partial_tu + P(D)u = 0$, where the symbol $P$ is real, homogeneous and nonsingular. We prove that for initial data $f\in H^s(\mathbb{R}^n)$ ... 
Reconstruction of the Derivative of the Conductivity at the Boundary
Ponce Vanegas, F. (201908)We describe a method to reconstruct the conductivity and its normal derivative at the boundary from the knowledge of the potential and current measured at the boundary. This boundary determination implies the uniqueness ... 
Static and Dynamical, Fractional Uncertainty Principles
Kumar, S.; Ponce Vanegas, F.; Vega, L. (202103)We study the process of dispersion of lowregularity solutions to the Schrödinger equation using fractional weights (observables). We give another proof of the uncertainty principle for fractional weights and use it to get ...