2020
DOI: 10.48550/arxiv.2001.07599
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Inverse problems for real principal type operators

Lauri Oksanen,
Mikko Salo,
Plamen Stefanov
et al.

Abstract: We consider inverse boundary value problems for general real principal type differential operators. The first results state that the Cauchy data set uniquely determines the scattering relation of the operator and bicharacteristic ray transforms of lower order coefficients. We also give two different boundary determination methods for general operators, and prove global uniqueness results for determining coefficients in nonlinear real principal type equations. The article presents a unified approach for treatin… Show more

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Cited by 11 publications
(19 citation statements)
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“…The separation matrix (53) corresponding to the functions v f k and points x k is invertible for ε ≤ ε 0 for ε 0 small enough. We set M := M ε 0 .…”
Section: Separation Of Pointsmentioning
confidence: 99%
See 1 more Smart Citation
“…The separation matrix (53) corresponding to the functions v f k and points x k is invertible for ε ≤ ε 0 for ε 0 small enough. We set M := M ε 0 .…”
Section: Separation Of Pointsmentioning
confidence: 99%
“…The research of inverse problems for non-linear equations is expanding fast. By using the higher-order linearization, inverse problems for nonlinear models have been studied for example in [3,11,12,13,16,17,21,20,32,36,37,38,41,45,46,53,60,62,63].…”
Section: Introductionmentioning
confidence: 99%
“…We mention that non-linear interactions have also been used to recover non-linear terms for scalar wave equations [33], scalar elliptic equations [13,31], and scalar real principal type equations [38]. In these four works, non-linear terms do not contain any derivatives, contrary to the Einstein and Yang-Mills equations.…”
Section: Introductionmentioning
confidence: 99%
“…The authors of [46] studied inverse problems for general semi-linear wave equations on Lorentzian manifolds, and in [45] they studied analogous problem for the Einstein-Maxwell equations. Recently, inverse problems for non-linear equations using the non-linearity as a tool, have been studied in [3,11,12,13,16,17,20,21,30,34,35,36,39,42,43,51,57,60,61]. The works mentioned above use the so-called higher order linearization method, which we will explain later.…”
mentioning
confidence: 99%