Now showing items 1-8 of 8

    • A Bilinear Strategy for Calderón's Problem 

      Ponce Vanegas, F.Autoridad BCAM (2019-08)
      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.Autoridad BCAM (2020-05)
      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.Autoridad BCAM; Ponce Vanegas, F.Autoridad BCAM (2021-01)
      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.Autoridad BCAM (2021-12-09)
      We construct counterexamples for the fractal Schrödinger convergence problem by combining a fractal extension of Bourgain's counterexample and the intermediate space trick of Du--Kim--Wang--Zhang. We confirm that the same ...
    • The Frisch–Parisi formalism for fluctuations of the Schrödinger equation 

      Kumar, S.; Ponce Vanegas, F.Autoridad BCAM; Roncal, L.Autoridad BCAM; Vega, L.Autoridad BCAM (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.Autoridad BCAM (2021-08-24)
      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 non-singular. 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.Autoridad BCAM (2019-08)
      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.Autoridad BCAM; Vega, L.Autoridad BCAM (2021-03)
      We study the process of dispersion of low-regularity 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 ...