We consider an inverse problem regarding the detection of small conductivity inhomogeneities in a boundary value problem for a semilinear elliptic equation. For such a problem, that is related to cardiac electrophysiology, an asymptotic expansion for the boundary potential due to the presence of small conductivity inhomogeneities was established in [4]. Starting from this we derive Lipschitz continuous dependence estimates for the corresponding inverse problem.
Cerutti M. C., Beretta E., Ratti L. (2021). Lipschitz stable determination of small conductivity inclusions in a semilinear equation from boundary data. MATHEMATICS IN ENGINEERING, 3(1), 1-10 [10.3934/mine.2021003].
Lipschitz stable determination of small conductivity inclusions in a semilinear equation from boundary data
Ratti L.
2021
Abstract
We consider an inverse problem regarding the detection of small conductivity inhomogeneities in a boundary value problem for a semilinear elliptic equation. For such a problem, that is related to cardiac electrophysiology, an asymptotic expansion for the boundary potential due to the presence of small conductivity inhomogeneities was established in [4]. Starting from this we derive Lipschitz continuous dependence estimates for the corresponding inverse problem.| File | Dimensione | Formato | |
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