This monograph deals with the solvability of the inversepotential problem in the two-dimensional case. A new method based on thetheory of boundary-value problems for analytic functions and univalentfunctions is constructed, and local existence theorems, a prioriestimates, and a parameter continuation method are established.Furthermore, the smoothness of the inverse problem solution isinvestigated.
The obtained results are applied to geologic interpretation ofgravitational and magnetic fields. The following sections ofmathematical analyses are used: harmonic functions; boundary-valueproblems for analytic functions; conformal mappings; non-linearanalysis; problems with unknown boundaries; moments theory; variationalinequality theory; ill-posed problems theory, in particular fordifferential equations; numerical methods.
This monograph will be of value and interest to mathematicians andgeophysicists working with this theory.
1996; viii+248 pages ISBN 90-6764-202-9 Price (all prices are subject to change without notice): EUR 156/US$ 223
