Global Identifiability of Low Regularity Fluid Parameters in Acoustic Tomography of Moving Fluid

Abstract

We are concerned with inverse boundary problems for first order perturbations of the Laplacian, which arise as model operators in the acoustic tomography of a moving fluid. We show that the knowledge of the Dirichletto-Neumann map on the boundary of a bounded domain in R n , n ≥ 3, determines the first order perturbation of low regularity up to a natural gauge transformation, which sometimes is trivial. As an application, we recover the fluid parameters of low regularity from boundary measurements, sharpening the regularity assumptions in the recent results of [1] and [3]. In particular, we allow some fluid parameters to be discontinuous.

Stability estimates for an inverse boundary value problem for biharmonic operators with first order perturbation from partial data

“…We highlight that unique recovery of the first order perturbation appearing in higher order elliptic operators differs from analogous problems for second order operators, such as the magnetic Schrödinger operator. In the latter case, due to the gauge invariance of boundary measurements, one can only hope to uniquely recover dA, which is the exterior derivative of the first order perturbation A, see for instance [25,29,34,39] and the references therein among the extensive literature in this direction. Here, if we view A as a 1-form, then dA is a 2-form given by the formula…”

Stability estimates in a partial data inverse boundary value problem for biharmonic operators at high frequencies

“…We highlight that unique recovery of the first order perturbation appearing in higher order elliptic operators differs from analogous problems concerning the Laplacian. In the latter case, one can only hope to recover dA, the exterior derivative of the first order perturbation A, due to the gauge invariance of boundary measurements, see for instance [22,25,28,32] and the references therein among the extensive literature in this direction. Here, if we view A as a 1-form, then dA is a 2-form given by the formula…”