Geodesic
An inverse overdetermined problem for a nonhomogeneous elastic medium
Sibirskij žurnal industrialʹnoj matematiki, Tome 7 (2004) no. 4, pp. 141-147 
A. A. Schwab. An inverse overdetermined problem for a nonhomogeneous elastic medium. Sibirskij žurnal industrialʹnoj matematiki, Tome 7 (2004) no. 4, pp. 141-147. http://geodesic.mathdoc.fr/item/SJIM_2004_7_4_a12/
@article{SJIM_2004_7_4_a12,
     author = {A. A. Schwab},
     title = {An inverse overdetermined problem for a~nonhomogeneous elastic medium},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {141--147},
     year = {2004},
     volume = {7},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2004_7_4_a12/}
}
TY  - JOUR
AU  - A. A. Schwab
TI  - An inverse overdetermined problem for a nonhomogeneous elastic medium
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2004
SP  - 141
EP  - 147
VL  - 7
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SJIM_2004_7_4_a12/
LA  - ru
ID  - SJIM_2004_7_4_a12
ER  - 
%0 Journal Article
%A A. A. Schwab
%T An inverse overdetermined problem for a nonhomogeneous elastic medium
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2004
%P 141-147
%V 7
%N 4
%U http://geodesic.mathdoc.fr/item/SJIM_2004_7_4_a12/
%G ru
%F SJIM_2004_7_4_a12

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a class of overdetermined problems in the theory of elasticity for which load and displacement vectors are specified on a surface. This class of problems arises in the detection of inhomogeneities of inclusion or crack type for a nonhomogeneous medium. On the basis of a previously introduced integral criterion, we prove a theorem on the uniqueness of the determination of the boundaries of inclusions and the elastic characteristics of the inclusions.

[1] Shvab A. A., “Nekorrektnye staticheskie zadachi teorii uprugosti”, Izv. AN SSSR. Mekhanika tverdogo tela, 1989, no. 6, 98–106

[2] Shvab A. A., “Suschestvenno pereopredelennaya zadacha teorii uprugosti”, Sib. zhurn. industr. matematiki, 4:1(7) (2001), 204–207 | MR | Zbl

[3] Almansi E., “Un teorema sulle deformation elastiche dei Solidi isotropi”, Rend. Accad. Lincei. 5 ser., 16 (1907), 865–868

[4] Novatskii V., Teoriya uprugosti, M., 1975