10 papers · 1 filter
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…
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…
Stability for an inverse flux and an inverse boundary coefficient problems
Mourad Choulli, Shuai Lu, Hiroshi Takase
We establish both Lipschitz and logarithmic stability estimates for an inverse flux problem and subsequently apply these results to an inverse boundary coefficient problem. Further…