An inverse stability result for non-compactly supported potentials by one arbitrary lateral Neumann observation

Bellassoued, Mourad; Kian, Yavar; Soccorsi, Éric

doi:10.1016/j.jde.2016.01.033

Cited by 23 publications

(32 citation statements)

References 46 publications

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“…Let us mention that inverse boundary value problems in an infinite slab were addressed by Yang in [Y] for bi-harmonic operators. Recently, several stability results were derived in [CS,Ki,KPS1,KPS2,BKS] for non compactly supported coefficients inverse problems in an infinite waveguide with a bounded cross section. More specifically, we refer to [KKS, CKS] for the analysis of inverse problems in the framework of a periodic cylindrical domain examined in this paper.…”

Section: Introductionmentioning

confidence: 99%

Stability result for elliptic inverse periodic coefficient problem by partial Dirichlet-to-Neumann map

2018

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Section: Introductionmentioning

confidence: 99%

Stability result for elliptic inverse periodic coefficient problem by partial Dirichlet-to-Neumann map

2018

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“…Let n be the outward unit normal vector of ∂Ω. 1 Since Ω is only subjected to the condition Ω ⊂ Ω 1 we may have Ω = Ω 1 this is why we use a different notation for the outward unit normal vector of Ω 1 and Ω. Before we state our result, let us also recall that for any A ∈ L ∞ (Ω) 3 satisfying div(A) ∈ L ∞ (Ω), we can define the trace map A · n as the unique element of…”

Section: Statement Of the Main Resultsmentioning

confidence: 99%

Determination of non-compactly supported electromagnetic potentials in an unbounded closed waveguide

Kian

2019

Rev. Mat. Iberoam.

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We study the inverse problem of determining a magnetic Schrödinger operator in an unbounded closed waveguide from boundary measurements. We consider this problem with a general closed waveguide in the sense that we only require our unbounded domain to be contained into an infinite cylinder. In this context we prove the unique recovery of the magnetic field and the electric potential associated with general bounded and non-compactly supported electromagnetic potentials. By assuming that the electromagnetic potentials are known on the neighborhood of the boundary outside a compact set, we even prove the unique determination of the magnetic field and the electric potential from measurements restricted to a bounded subset of the infinite boundary. Finally, in the case of a waveguide taking the form of an infinite cylindrical domain, we prove the recovery of the magnetic field and the electric potential from partial data corresponding to restriction of Neumann boundary measurements to slightly more than half of the boundary. We establish all these results by mean of a new class of complex geometric optics solutions and of Carleman estimates suitably designed for our problem stated in an unbounded domain and with bounded electromagnetic potentials.

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“…In this section we will complete the proof of Theorem 1.1. We fix q = q 2 − q 1 on and we extend it by q = 0 on R 3 \ . We assume that the constant ε given in the beginning of § 4 is chosen in such a way that for any θ ∈ {y ∈ S 1 : |y − θ 0 | ε} we have ∂ω −,ε,θ ⊂ G .…”

Section: Uniqueness Resultsmentioning

confidence: 99%

Recovery of Non-Compactly Supported Coefficients of Elliptic Equations on an Infinite Waveguide

Kian¹

2018

J. Inst. Math. Jussieu

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We consider the unique recovery of a non compactly supported and non periodic perturbation of a Schrödinger operator in an unbounded cylindrical domain, also called waveguide, from boundary measurements. More precisely, we prove recovery of general class of electric potentials from the partial Dirichlet-to-Neumann map, where the Dirichlet data is supported on slightly more than half of the boundary and the Neumann data is taken on the other half of the boundary. We apply this result in different context including recovery of some general class of coefficients from measurements on a bounded subset and recovery of an electric potential, supported on an unbounded cylinder, of a Schrödinger operator in a slab.

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An inverse stability result for non-compactly supported potentials by one arbitrary lateral Neumann observation

Cited by 23 publications

References 46 publications

Stability result for elliptic inverse periodic coefficient problem by partial Dirichlet-to-Neumann map

Stability result for elliptic inverse periodic coefficient problem by partial Dirichlet-to-Neumann map

Determination of non-compactly supported electromagnetic potentials in an unbounded closed waveguide

Recovery of Non-Compactly Supported Coefficients of Elliptic Equations on an Infinite Waveguide

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