Inverse Problems and Carleman Estimates: Global Uniqueness, Global Convergence and Experimental Data

Preface
Acknowledgments
Contents
1 Topics of this book
2 Carleman estimates and Hölder stability for ill-posed Cauchy problems
3 Global uniqueness for coefficient inverse problems and Lipschitz stability for a hyperbolic CIP
4 The quasi-reversibility numerical method for ill-posed Cauchy problems for linear PDEs
5 Convexification for ill-posed Cauchy problems for quasi-linear PDEs
6 A special orthonormal basis in L2(a, b) for the convexification for CIPs without the initial conditions—restricted Dirichlet-to-Neumann map
7 Convexification of electrical impedance tomography with restricted Dirichlet-to-Neumann map data
8 Convexification for a coefficient inverse problem for a hyperbolic equation with a single location of the point source
9 Convexification for an inverse parabolic problem
10 Experimental data and convexification for the recovery of the dielectric constants of buried targets using the Helmholtz equation
11 Travel time tomography with formally determined incomplete data in 3D
12 Numerical solution of the linearized travel time tomography problem with incomplete data
Bibliography
Index