Lipschitz stability for the electrostatic inverse boundary value problem with piecewise linear conductivities

Abstract

We consider the electrostatic inverse boundary value problem also known as electrical impedance tomography (EIT) for the case where the conductivity is a piecewise linear function on a domain $\Omega \subset {\mathbb{R}}^n$ and we show that a Lipschitz stability estimate for the conductivity in terms of the local Dirichlet-to-Neumann map holds true.

28 pages. arXiv admin note: text overlap with arXiv:1405.0475

References in corpus (1)

• Lipschitz continuous dependence of piecewise constant Lamé coefficients from boundary data: the case of non flat interfaces

Cited by in corpus (12)

• Uniqueness and Lipschitz stability in Electrical Impedance Tomography with finitely many electrodes
• Monotonicity-based inversion of the fractional Schrödinger equation II. General potentials and stability
• Uniqueness for the electrostatic inverse boundary value problem with piecewise constant anisotropic conductivities
• Global uniqueness and Lipschitz-stability for the inverse Robin transmission problem
• Infinite-dimensional inverse problems with finite measurements
• Calderón's Inverse Problem with a Finite Number of Measurements
• Uniqueness, stability and global convergence for a discrete inverse elliptic Robin transmission problem
• Inverse problems on low-dimensional manifolds
• Calderón's Inverse Problem with a Finite Number of Measurements II: Independent Data
• Lipschitz stability estimate for the simultaneous recovery of two coefficients in the anisotropic Schrödinger type equation via local Cauchy data
• Continuous Generative Neural Networks: A Wavelet-Based Architecture in Function Spaces
• Local recovery of a piecewise constant anisotropic conductivity in EIT on domains with exposed corners