Prefaee to the Second Edition PrefacetotheFirstEdifion Chapter l Inverse Problems 1．1 The inverse problem of gravimetry 1．2 The lnverse conductivity problem 1．3 Inverse scattering 1．4 Tomography and the inverse seismic problem 1．5 Inverse spectral problems Chapter 2 Ill-Posed Problems and Regularization 2．1 Well．and ill—posed problems 2．2 Conditional correctness：Regularization 2．3 Construetion of regularizers 2．4 Convergence of regularization algorithms 2．5 herative algorithms Chapter 3 Uniqueness and Stability in the Cauchy Problem 3．1 The backward parabolic equation 3．2 General Carleman estimates and the Cauchy problem 3．3 Elliptic and parabolic equations 3．4 Hyperbolic and Schr6dinger equations 3．5 Systems of partial differential equations 3．6 Open problems Chapter 4 Elliptic Equations：Single Boundary Measurements 4．0 Results on elliptic boundary value problems 4．1 Inverse gravimetry 4．2 Reconstruction of lowcr-order terms 4．3 The jBVeFSC conductivity problem 4．4 Methods of the theory of one complex variable 4．5 Linearization of the coe佑cients problem 4．6 Some problems ofdetection ofdefects 4．7 Open problems Chapter 5 Elliptic Equations：Many Boundary Measurements 5．O The Dirichlet．to—Neumann map 5．1 Boundary reconstruction 5．2 Reconstruction in Q 5．3 Completeness of products of solutions of PDE 5．4 Recovery of several coeffcients 5．5 The plane case 5．6 Nonlinear equations 5．7 Discontinuous conductivities 5．8 Maxwell』s and elasticity systems 5．9 Open problems Chapter 6 Scattering Problems 6．0 Direct Scattering 6 l From A to nearfield 6 2 Scattering by a medium 6．3 Scattering by obstacles 6．4 Open problems Chapter 7 Integral Geometry and Tomography 7．1 The Radon transfofin and its inverse 7．2 The energy integral methods
7 3 Boman』s counterexample 7．4 The transport equation 7．5 Open problems Chapter 8 Hyperbolic Problems 8．0 Introduction 8．1 The one．dimensional case 8．2 Single boundary measurements 8．3 Many measurements：use of beam solutions 8．4 Many measurements：methods of boundary control 8．5 Recovery ofdiscontinuity ofthe speed ofpropagation 8．6 Open problems Chapter 9 Inverse parabolic problems 9．0 Introduction 9．1 Final orerdetermination 9．2 Lateral orerdetermination：single measurements 9．3 ne inverse problem of option pricing 9．4 Lateral overdetermination：many measurements 9．5 Discontinuous principal coeMcient and recovery of a domain 9．6 Nonlinear equations 9．7 Interior sources 9．8 Open problems Chapter 10 Some Numerical Methods 10．1 Linearization 10．2 Variational regularization of the Cauchy problem 1O．3 Relaxation methods 10．4 Layer-stripping 10．5 Range test algorithms 10．6 Discrete methods Appendix．Funcfion~Spaces References Index
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