Now showing items 1-8 of 8

• #### A Bilinear Strategy for Calderón's Problem ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ...

(2022)
• #### Reconstruction of the Derivative of the Conductivity at the Boundary ﻿

(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 ﻿

(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 ...