A boundary integral equation for Calderón's inverse conductivity problem.

Kari Astala; Lassi Päivärinta

Collectanea Mathematica (2006)

  • Volume: 57, Issue: Extra, page 127-139
  • ISSN: 0010-0757

Abstract

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Towards a constructive method to determine an L∞-conductivity from the corresponding Dirichlet to Neumann operator, we establish a Fredholm integral equation of the second kind at the boundary of a two dimensional body. We show that this equation depends directly on the measured data and has always a unique solution. This way the geometric optics solutions for the L∞-conductivity problem can be determined in a stable manner at the boundary and outside of the body.

How to cite

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Astala, Kari, and Päivärinta, Lassi. "A boundary integral equation for Calderón's inverse conductivity problem.." Collectanea Mathematica 57.Extra (2006): 127-139. <http://eudml.org/doc/41788>.

@article{Astala2006,
abstract = {Towards a constructive method to determine an L∞-conductivity from the corresponding Dirichlet to Neumann operator, we establish a Fredholm integral equation of the second kind at the boundary of a two dimensional body. We show that this equation depends directly on the measured data and has always a unique solution. This way the geometric optics solutions for the L∞-conductivity problem can be determined in a stable manner at the boundary and outside of the body.},
author = {Astala, Kari, Päivärinta, Lassi},
journal = {Collectanea Mathematica},
keywords = {Ecuaciones diferenciales elípticas; Ecuaciones integrales; Problemas inversos; Operadores de Fredholm; boundary data; complex geometric optics solutions; Dirichlet to Neumann operator; Fredholm integral equation of the second kind},
language = {eng},
number = {Extra},
pages = {127-139},
title = {A boundary integral equation for Calderón's inverse conductivity problem.},
url = {http://eudml.org/doc/41788},
volume = {57},
year = {2006},
}

TY - JOUR
AU - Astala, Kari
AU - Päivärinta, Lassi
TI - A boundary integral equation for Calderón's inverse conductivity problem.
JO - Collectanea Mathematica
PY - 2006
VL - 57
IS - Extra
SP - 127
EP - 139
AB - Towards a constructive method to determine an L∞-conductivity from the corresponding Dirichlet to Neumann operator, we establish a Fredholm integral equation of the second kind at the boundary of a two dimensional body. We show that this equation depends directly on the measured data and has always a unique solution. This way the geometric optics solutions for the L∞-conductivity problem can be determined in a stable manner at the boundary and outside of the body.
LA - eng
KW - Ecuaciones diferenciales elípticas; Ecuaciones integrales; Problemas inversos; Operadores de Fredholm; boundary data; complex geometric optics solutions; Dirichlet to Neumann operator; Fredholm integral equation of the second kind
UR - http://eudml.org/doc/41788
ER -

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