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Zbl 1034.35148
Alessandrini, Giovanni; Beretta, Elena; Rosset, Edi; Vessella, Sergio
Optimal stability for inverse elliptic boundary value problems with unknown boundaries. (English)
[J] Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 29, No. 4, 755-806 (2000). ISSN 0391-173X

A class of inverse problems associated to an elliptic boundary value problem in high dimension is studied. The location of inaccessible parts in the boundary by measuring Dirichlet (resp. Neumann) data on an accessible place $A$ for given Neumann (resp. Dirichlet) data supported in $A$ is determined and the best possible stability estimates for the location are given. The results have applications in other applied sciences such as material science and physics.
[Shigui Ruan (Coral Glabes)]

MSC 2000:: *35R30 Inverse problems for PDE
35J25 Second order elliptic equations, boundary value problems
31B20 Boundary value and inverse problems (higher-dim. potential theory)
35B60 Continuation of solutions of PDE
35R25 Improperly posed problems for PDE

Keywords: location of inaccessible parts; Dirichlet data; Neumann data; stability estimates

Cited in: Zbl 1206.35252

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