Stability estimates for the inverse boundary value problem for the biharmonic operator with bounded potentials

Abstract

Please cite this article in press as: A.P. Choudhury, V.P. Krishnan, Stability estimates for the inverse boundary value problem for the biharmonic operator with bounded potentials, J. Math. Anal. Appl. (2015), http://dx. AbstractIn this article, stability estimates are given for the determination of the zeroth-order bounded perturbations of the biharmonic operator when the boundary Neumann measurements are made on the whole boundary and on slightly more than half the boundary, respectively. For the case of measurements on the whole boundary, the stability estimates are of ln-type and for the case of measurements on slightly more than half of the boundary, we derive estimates that are of ln ln-type.

Inverse Boundary Value Problem of Determining Up to a Second Order Tensor Appear in the Lower Order Perturbation of a Polyharmonic Operator

“…Inverse problems concerning higher order operators is an active field of research in recent days. It addresses the recovery of the coefficient from measurements taken on full or on a part of the boundary [16,17,19,20,13,14,5,6], lower regularity of the coefficients [21,3,4], stability issues [10,9] from the boundary Dirichlet-Neumann data. In this paper we are interested in the recovery of the coefficients in (1.1) from the boundary Dirichlet-Neumann data.…”

“…10) where ω, ω ∈ R n are such that ω · ω = 0 and | ω| = |ω|. Observe that ϕ and ψ solves the Eikonal equation p 0,ϕ (x, ∇ψ) = 0 in Ω, that is |∇ϕ| = |∇ψ| and ∇ϕ · ∇ψ = 0.…”

Inverse boundary value problems for polyharmonic operators with non-smooth coefficients

“…The result of Assylbekov and Iyer is in the spirit of the work of the first author and Torres [10] who studied the inverse conductivity problem for conductivities with 3/2 derivatives. The stability of the solution of this problem was considered by Choudhury and Krishnan [14]. We also mention work of Bhattarcharyya and Ghosh [5] who consider operators where the principal part is the polyharmonic operator and the operators includes terms of second order.…”

Inverse boundary value problems for polyharmonic operators with non-smooth coefficients

“…The study of inverse boundary value problems for the biharmonic operator was begun by Krupchyk, Lassas and Uhlmann [22] who establish that first order terms are uniquely determined by the Cauchy data. The stability of the solution of this problem was considered by Choudhury and Krishnan [15]. Krupchyk, Lassas and Uhlmann [21] study inverse boundary value problems for the biharmonic operators with partial data on the boundary.…”