Lipschitz stable determination of small conductivity inclusions in a semilinear equation from boundary data.

Elena Beretta; M. Cristina Cerutti; Luca Ratti

Lipschitz stable determination of small conductivity inclusions in a semilinear equation from boundary data.

Elena Beretta, M. Cristina Cerutti, Luca Ratti

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	1-10
Journal	Mathematics in Engineering
State	Published - 2021

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title = "Lipschitz stable determination of small conductivity inclusions in a semilinear equation from boundary data.",

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.",

author = "Elena Beretta and Cerutti, {M. Cristina} and Luca Ratti",

year = "2021",

language = "English (US)",

pages = "1--10",

journal = "Mathematics in Engineering",

publisher = "AIMS Press",

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TY - JOUR

T1 - Lipschitz stable determination of small conductivity inclusions in a semilinear equation from boundary data.

AU - Beretta, Elena

AU - Cerutti, M. Cristina

AU - Ratti, Luca

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

M3 - Article

SP - 1

EP - 10

JO - Mathematics in Engineering

JF - Mathematics in Engineering

ER -

Lipschitz stable determination of small conductivity inclusions in a semilinear equation from boundary data.

Abstract

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