11 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…
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.
Quantitative Borg-Levinson theorem for the magnetic Schödinger operator with unbounded electrical potential
Mourad Choulli, Hiroshi Takase
The first author established in [8] a quantitative Borg-Levinson theorem for the Schrödinger operator with unbounded potential. In the present work, we extend the results in [8] t…
Stable determination of the potential for the Helmholtz equation in the high frequency limit from boundary measurements
Mourad Choulli, Hiroshi Takase
We establish a triple logarithmic stability estimate of determining the potential in a Helmholtz equation from a partial Dirichlet-to-Neumann map in the high frequency limit. This…