Effectivized Holder-logarithmic stability estimates for the Gel'fand inverse problem

Abstract

We give effectivized Holder-logarithmic energy and regularity dependent stability estimates for the Gel'fand inverse boundary value problem in dimension $d=3$. This effectivization includes explicit dependance of the estimates on coefficient norms and related parameters. Our new estimates are given in $L^2$ and $L^{\infty }$ norms for the coefficient difference and related stability efficiently increases with increasing energy and/or coefficient difference regularity. Comparisons with preceeding results are given.

References in corpus (3)

• The d-bar approach to approximate inverse scattering at fixed energy in three dimensions
• A global stability estimate for the Gel'fand-Calderon inverse problem in two dimensions
• New global stability estimates for the Gel'fand-Calderon inverse problem

Cited by in corpus (2)

• Increasing stability for the inverse problem for the Schrödinger equation
• High frequency stability estimates for a partial data inverse problem