19 papers
Determination of separable perturbations of an unbounded potential in the two-dimensional Schrödinger equation
Mourad Choulli, Hiroshi Takase
We establish uniqueness and stability results for a class of perturbations of an unbounded potential in the two-dimensional Schrödinger equation, from the corresponding Dirichlet-t…
Quantitative strong unique continuation for the Schrödinger operator with unbounded potential
Mourad Choulli
We revisit \cite[Theorem 6.3]{JK}. By following the main ideas used to prove that theorem, we establish a quantitative version of strong unique continuation for the Schrödinger op…
Determining an Iwatsuka Hamiltonian by knowledge of its first band function
Mourad Choulli, Nour Kerraoui, Eric Soccorsi
We investigate the inverse problem of retrieving the magnetic potential of an Iwatsuka Hamiltonian through knowledge of its first band function. We prove that two magnetic potentia…
New quantitative unique continuation result for elliptic equations
Mourad Choulli, Hiroshi Takase
We prove a new quantitative unique continuation result for elliptic equations from Cauchy data. We provide a simple and direct proof based only on a Carleman inequality. Similar re…
Functional analysis and partial differential equations in spectral Barron spaces
Mourad Choulli, Shuai Lu, Hiroshi Takase
Spectral Barron spaces, constituting a specialized class of function spaces that serve as an interdisciplinary bridge between mathematical analysis, partial differential equations…
An - Carleman inequality for
Mourad Choulli, Hiroshi Takase
In this note, by refining the proof of the Carleman inequality obtained by Dos Santos, Kenig, and Salo in 2013, we establish a new - Carleman inequality.