2021
DOI: 10.1016/j.aim.2021.107956
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The Calderón inverse problem for isotropic quasilinear conductivities

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Cited by 34 publications
(31 citation statements)
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“…One of these difficulties comes from the fact that the parabolic equation studied here is not self adjoint as opposed to the self adjoint elliptic equation studied in [4]. This makes some of the symmetries present in the latter work to disappear as is apparent already from the statement of our Proposition 1.1 compared to the analogous proposition in [4]. Secondly, the form of the geometric optics solutions here are rather different from the complex geometric optics solutions constructed in [4].…”
Section: Introductionmentioning
confidence: 81%
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“…One of these difficulties comes from the fact that the parabolic equation studied here is not self adjoint as opposed to the self adjoint elliptic equation studied in [4]. This makes some of the symmetries present in the latter work to disappear as is apparent already from the statement of our Proposition 1.1 compared to the analogous proposition in [4]. Secondly, the form of the geometric optics solutions here are rather different from the complex geometric optics solutions constructed in [4].…”
Section: Introductionmentioning
confidence: 81%
“…A second order linearization method was considered by Sun and Uhlmann in [45] while the idea of higher order linearization was fully utilized by Kurylev, Lassas and Uhlmann in [33] to solve challenging inverse problems for hyperbolic equations. Without being exhaustive, we refer the reader for example to the works [13,17,28,33,35,37] that study inverse problems for nonlinear hyperbolic equations, [7,14,19,24,25,31,32,36,44] for some results concerning semilinear elliptic equations as well as [3,4,5,16,22,29,40,43,45] for results on quasilinear elliptic equations. All these works are based on the linearization method.…”
Section: Introductionmentioning
confidence: 99%
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