Abstract
In this paper we obtain essentially best possible stability estimates for a class of inverse problems associated to elliptic boundary value problems in which the role of the unknown is played by an inaccessible part of the boundary and the role of the data is played by overdetermined boundary data for the elliptic equation assigned on the remaining, accessible, part of the boundary. We treat the case of arbitrary space dimension n ≥ 2. Such problems arise in applied contexts of nondestructive testing of materials for either electric or thermal conductors, and are known to be ill-posed.
| Original language | French |
|---|---|
| Pages (from-to) | 607-611 |
| Number of pages | 5 |
| Journal | Comptes Rendus de l'Academie de Sciences - Serie IIb: Mecanique |
| Volume | 328 |
| Issue number | 8 |
| DOIs | |
| State | Published - Jan 1 2000 |
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Keywords
- Cavity
- Corrosion
- Inverse boundary value problems
- Stability
- Unique continuation
ASJC Scopus subject areas
- Geotechnical Engineering and Engineering Geology
Cite this
Problèmes inverses à frontières inconnues : Stabilité optimale. / Alessandrini, Giovanni; Beretta, Elena; Rosset, Edi; Vessella, Sergio.
In: Comptes Rendus de l'Academie de Sciences - Serie IIb: Mecanique, Vol. 328, No. 8, 01.01.2000, p. 607-611.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Problèmes inverses à frontières inconnues
T2 - Stabilité optimale
AU - Alessandrini, Giovanni
AU - Beretta, Elena
AU - Rosset, Edi
AU - Vessella, Sergio
PY - 2000/1/1
Y1 - 2000/1/1
N2 - In this paper we obtain essentially best possible stability estimates for a class of inverse problems associated to elliptic boundary value problems in which the role of the unknown is played by an inaccessible part of the boundary and the role of the data is played by overdetermined boundary data for the elliptic equation assigned on the remaining, accessible, part of the boundary. We treat the case of arbitrary space dimension n ≥ 2. Such problems arise in applied contexts of nondestructive testing of materials for either electric or thermal conductors, and are known to be ill-posed.
AB - In this paper we obtain essentially best possible stability estimates for a class of inverse problems associated to elliptic boundary value problems in which the role of the unknown is played by an inaccessible part of the boundary and the role of the data is played by overdetermined boundary data for the elliptic equation assigned on the remaining, accessible, part of the boundary. We treat the case of arbitrary space dimension n ≥ 2. Such problems arise in applied contexts of nondestructive testing of materials for either electric or thermal conductors, and are known to be ill-posed.
KW - Cavity
KW - Corrosion
KW - Inverse boundary value problems
KW - Stability
KW - Unique continuation
UR - http://www.scopus.com/inward/record.url?scp=0012041748&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0012041748&partnerID=8YFLogxK
U2 - 10.1016/S1620-7742(00)00011-8
DO - 10.1016/S1620-7742(00)00011-8
M3 - Article
AN - SCOPUS:0012041748
VL - 328
SP - 607
EP - 611
JO - Comptes Rendus de l'Academie de Sciences - Serie IIb: Mecanique
JF - Comptes Rendus de l'Academie de Sciences - Serie IIb: Mecanique
SN - 1620-7742
IS - 8
ER -