Optimal stability for inverse elliptic boundary value problems with unknown boundary
Optimal stability for inverse elliptic boundary value problems with unknown boundary
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.
- University of Florence Italy
- University of Trieste Italy
Inverse problems for PDEs, inverse problems, unknown boundarie, Neumann data, Stability estimates; Quantitative Estimates of Unique Continuation; Inverse Problems; elliptic Equations, stability, location of inaccessible parts, unknown boundaries; stability; inverse problems, Boundary value problems for second-order elliptic equations, stability estimates, Dirichlet data, Ill-posed problems for PDEs, Boundary value and inverse problems for harmonic functions in higher dimensions, Continuation and prolongation of solutions to PDEs
Inverse problems for PDEs, inverse problems, unknown boundarie, Neumann data, Stability estimates; Quantitative Estimates of Unique Continuation; Inverse Problems; elliptic Equations, stability, location of inaccessible parts, unknown boundaries; stability; inverse problems, Boundary value problems for second-order elliptic equations, stability estimates, Dirichlet data, Ill-posed problems for PDEs, Boundary value and inverse problems for harmonic functions in higher dimensions, Continuation and prolongation of solutions to PDEs
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