Multiscale Potential Theory

"The book is devoted to well-posed and ill-posed boundary-value problems arising in geoscience, elasticity, gravimetry and other areas, including satellite problems. New mathematical methods and fast computational schemes based on harmonic analysis and wavelet transforms are developed... The book may be used for graduate-level courses in geomathematics, applied mathematics, and geophysics. It is also an up-to-date reference text for geoscientists, applied mathematicians, and engineers." -Zentralblatt MATH "Potential theory is a classical area in mathematics which for over 200 years has attracted and still attracts attention. Famous mathematicians have contributed. At the beginning of the 19th century it was Laplace, Poisson, Gauss, Green, both F. and C. Neumann, Helmholtz, Dirichlet and others. In the last century axiomatic, fine, probabilistic, discrete, and nonlinear potential theory arose. The present book is written for applications in geodesy and geophysics and is hence devoted to classical potential theory with particular attention to wavelet approximation... Each chapter is concluded with exercises which have solution hints at the end of the book... The book is a self-contained and unique presentation of multiscale potential theory, interesting for applied mathematicians, geophysicists, etc. and proper even for students." -Mathematical Reviews

• 1 Introduction.- 2 Preliminary Tools.- 2.1 Basic Settings.- 2.2 Spherical Nomenclature.- 2.3 Sphere Oriented Potential Theory.- 2.4 Exercises.- I Well-Posed Problems.- 3 Boundary-Value Problems of Potential Theory.- 4 Boundary-Value Problems of Elasticity.- II Ill-Posed Problems.- 5 Satellite Problems.- 6 The Gravimetry Problem.- 7 Conclusion.- 8 Hints for the Solution of the Exercises.- References.