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.

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Cited by in corpus (5)

• Verification of a variational source condition for acoustic inverse medium scattering problems
• Variational source conditions and stability estimates for inverse electromagnetic medium scattering problems
• Increasing stability for the inverse problem for the Schrödinger equation
• Hölder-logarithmic stability in Fourier synthesis
• High frequency stability estimates for a partial data inverse problem