Stability in the determination of the coefficients for coupled relativistic Schr\"odinger system

Abstract

In this article, we prove a stability result for the identification of the coefficients appearing in a coupled relativistic Schr\"odinger system posed on a bounded domain of $\mathbb{R}^{1+n}$, where $n \geq 3$. More precisely, by utilizing input-output operator, where Neumann boundary data are available only on a subset of the boundary, and constructing an appropriate geometric optics solution, we derive a stability estimate of $\log$-$\log$ type for the matrix-valued first-order coefficients. This result is subsequently used to obtain a $\log$-$\log$-$\log$ type stability estimate for the zeroth-order matrix-valued potential.