TITLE:
An Explicit Formula of the Dirichlet-to-Neumann Map for a Radial Potential in Dimension 3
AUTHORS:
Fagueye Ndiaye
KEYWORDS:
Calderón’s Problem, Schrödinger Operator, Potential, Inverse Potential Problem, Dirichlet-to-Neuman Map, Numerical Simulations, Lipschitz Stability
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.2,
February
21,
2022
ABSTRACT: In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for the Schrödinger equation in 3-dimensional. We numerically implement the coefficients of the explicit formulas. In this work, Lipschitz type stability is established near the edge of the domain with giving estimation constant. That is necessary for the reconstruction of the potential from Dirichlet-to-Neuman map.