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 ...

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 ...

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 $f\in H^s(\mathbb{R}^n)$ ...

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 ...

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 ...

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 ...

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 ...