Inverse Problems In Mathematical Physics: Proceedings Of The Lapland Conference On Inverse Problems Held At Saariselkä, Finland, 14-20 June 1992 (lecture Notes In Physics)

The book contains presentations of recent and ongoing research on inverse problems and its application to engineering and physical sciences. The articles are structured around three closely related topics: Inverse scattering problems, inverse boundary value problems, and inverse spectral problems. The applications range from quantum and electromagnetic scattering to medical imaging, geophysical sounding of the Earth, and non-destructive material evaluation. The book gives an up-to-date presentation of the most recent developments in these rapidlychanging and evolving fields of applied research. The contributors of the volume give extra emphysis to the pedagogical aspects of their presentation to make this collection eysily accessible to graduate students as well as to people working on nearby fields of research. Introduction....Pages ix-xviii Stability for the crack determination problem....Pages 1-8 Layer-stripping reconstruction algorithms in impedance imaging....Pages 9-15 Determination of the inhomogeneous term in evolution equations....Pages 16-21 Target signatures for Maxwell's equations....Pages 22-28 The use of Graßmann identities for inversion of a general model in diffuse tomography....Pages 29-48 Generic uniqueness and stability in some inverse parabolic problem....Pages 49-54 Regularization — Analytic and stochastic aspects....Pages 55-61 Problems in impedance imaging....Pages 62-70 Uniqueness for inverse problems in quasilinear differential equations....Pages 71-86 Diffraction by periodic structures....Pages 87-102 On uniqueness in inverse obstacle scattering....Pages 103-111 The inverse Scattering Problem for a homogeneous Bi-isotropic Slab Using Transient data....Pages 112-125 On the inverse scattering problem for rational reflection coefficients....Pages 126-133 Some geometric aspects of multidimensional inverse spectral problems....Pages 134-138 Three dimensional time harmonic inverse electromagnetic scattering....Pages 139-147 Determination of a radially symmetric speed of sound from transmission eigenvalues....Pages 148-156 A finite difference method for the inverse scattering problem at fixed frequency....Pages 157-166 Present status of the generalized Marchenko method for the solution of the inverse scattering problem in three dimensions....Pages 167-173 Inverse spectral problems in riemannian geometry....Pages 174-182 Local results for a two dimensional inverse conductivity problem....Pages 183-188 Inverse scattering at fixed energy for exponentially decreasing potentials....Pages 189-192 Inverse problems related to integrable nonlinear partial differential equations....Pages 193-202 Some estimates of green function and applications in inverse scattering theory for the Schrödinger operator with a singular potential....Pages 203-206 Reconstruction of electromagnetic parameters from boundary measurements....Pages 207-215 Inverse boundary value problems for Schrödinger operators....Pages 216-230 Linearizations of anisotropic inverse problems....Pages 231-241 Optimal parameter choice for Tikhonov regularization in Hilbert scales....Pages 242-250 Identification of the filtration coefficient....Pages 251-256 This volume contains presentations of research on three aspects of inverse problems: inverse scattering; inverse boundary values; and inverse spectral problems. The applications of inverse problems to a range of fields in the engineering and physical sciences are also discussed.