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Optimal stability for inverse elliptic boundary value problems with unknown boundaries. (English) Zbl 1034.35148

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.

MSC:

35R30 Inverse problems for PDEs
35J25 Boundary value problems for second-order elliptic equations
31B20 Boundary value and inverse problems for harmonic functions in higher dimensions
35B60 Continuation and prolongation of solutions to PDEs
35R25 Ill-posed problems for PDEs
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