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

Elena Beretta; M. Cristina Cerutti; Luca Ratti

doi:10.3934/mine.2021003

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

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
Number of pages	10
Journal	Mathematics In Engineering
Volume	3
Issue number	1
DOIs	https://doi.org/10.3934/mine.2021003
State	Published - 2021

Keywords

Inverse problem
Semilinear elliptic equation
Stability estimate

ASJC Scopus subject areas

Analysis
Mathematical Physics
Applied Mathematics

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10.3934/mine.2021003

Cite this

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

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.",

keywords = "Inverse problem, Semilinear elliptic equation, Stability estimate",

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

year = "2021",

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

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.

KW - Inverse problem

KW - Semilinear elliptic equation

KW - Stability estimate

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IS - 1

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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