Stable determination of boundaries from cauchy data

Elena Beretta, S. Vessella

Research output: Contribution to journalArticle

Abstract

The problem of determining a portion Γ of the boundary of a bounded planar domain Ω from Cauchy data arises in several contexts, for example, such as in corrosion detection from electrostatic measurements. We investigate this severely ill-posed problem establishing logarithmic continuous dependence of Γ from Cauchy data.

Original languageEnglish (US)
Pages (from-to)220-232
Number of pages13
JournalSIAM Journal on Mathematical Analysis
Volume30
Issue number1
DOIs
StatePublished - Jan 1 1998

Fingerprint

Cauchy
Electrostatics
Corrosion
Continuous Dependence
Ill-posed Problem
Logarithmic
Context

Keywords

  • Inverse problems
  • Stability

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

Stable determination of boundaries from cauchy data. / Beretta, Elena; Vessella, S.

In: SIAM Journal on Mathematical Analysis, Vol. 30, No. 1, 01.01.1998, p. 220-232.

Research output: Contribution to journalArticle

@article{a49c422063d1430a8500ced604ba6ec2,
title = "Stable determination of boundaries from cauchy data",
abstract = "The problem of determining a portion Γ of the boundary of a bounded planar domain Ω from Cauchy data arises in several contexts, for example, such as in corrosion detection from electrostatic measurements. We investigate this severely ill-posed problem establishing logarithmic continuous dependence of Γ from Cauchy data.",
keywords = "Inverse problems, Stability",
author = "Elena Beretta and S. Vessella",
year = "1998",
month = "1",
day = "1",
doi = "10.1137/S0036141097325733",
language = "English (US)",
volume = "30",
pages = "220--232",
journal = "SIAM Journal on Mathematical Analysis",
issn = "0036-1410",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "1",

}

TY - JOUR

T1 - Stable determination of boundaries from cauchy data

AU - Beretta, Elena

AU - Vessella, S.

PY - 1998/1/1

Y1 - 1998/1/1

N2 - The problem of determining a portion Γ of the boundary of a bounded planar domain Ω from Cauchy data arises in several contexts, for example, such as in corrosion detection from electrostatic measurements. We investigate this severely ill-posed problem establishing logarithmic continuous dependence of Γ from Cauchy data.

AB - The problem of determining a portion Γ of the boundary of a bounded planar domain Ω from Cauchy data arises in several contexts, for example, such as in corrosion detection from electrostatic measurements. We investigate this severely ill-posed problem establishing logarithmic continuous dependence of Γ from Cauchy data.

KW - Inverse problems

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=0032271479&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032271479&partnerID=8YFLogxK

U2 - 10.1137/S0036141097325733

DO - 10.1137/S0036141097325733

M3 - Article

AN - SCOPUS:0032271479

VL - 30

SP - 220

EP - 232

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

SN - 0036-1410

IS - 1

ER -