Inverse Logarithmic Potential Problem

Part 1 Formulation of inverse logarithmic potential problem - fundamental equation: formulation of inverse problem; nonlinear boundary value problem for mapping function; the analytic continuation of the potential across a boundary; the boundary analyticity of domain is a solution to an inverse problem; the structure of inverse problem solution, final solvability, examples. Part 2 Local solvability of an inverse problem: univalent function variation; local theorem of existence; linearization of the boundary value problem; the auxiliary problem; the Newton-Kantorovitch method; the explicit solution of the linear problem; the local uniqueness theorem; the density variation - the equivalent solution set of the inverse problems - remarks; the complex-valued density case; existence theorems for the inverse problems for small constant densities; proof of theorems. Part 3 The estimate of bounded univalent function co-efficients and univalent polynomials. Part 4 Mass potential estimates - necessary conditions of solvability - a priori estimates for inverse problem solution. Part 5 The continuation by the parameter of an inverse problem solution. Part 6 On the analyticity and smoothness of an inverse problem solution. Part 7 Inverse linear problem - determination of a density of the given domain by its exterior potential. Part 8 Conjugation of harmonic and analytic functions - direct and inverse problems. Part 9 Applications in gravity prospecting and in magnetic prospecting. (Part contents)