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Inverse logarithmic potential problem
Autor: Chedrednichenko V. G.
Rok: 1996.
ISBN: 9783110900125
OCLC Number: (OCoLC)922950426
OCLC Number: (ocolc)922950426
OKCZID: 110726885
Citace (dle ČSN ISO 690):
CHEREDNICHENKO, V. G. Inverse logarithmic potential problems. Utrecht: VSP, 1996. iii, 247 s. Inverse and ill-posed problems series.
Anotace
This monograph deals with the solvability of the inverse potential problem in the two-dimensional case. A new method based on the theory of boundary-value problems for analytic functions and univalent functions is constructed, and local existence theorems, a priori estimates, and a parameter continuation method are established. Furthermore, the smoothness of the inverse problem solution is investigated. The obtained results are applied to geologic interpretation of gravitational and magnetic fields. The following sections of mathematical analyses are used: harmonic functions; boundary-value problems for analytic functions; conformal mappings; non-linear analysis; problems with unknown boundaries; moments theory; variational inequality theory; ill-posed problems theory, in particular for differential equations; and numerical methods. This monograph should be of interest to mathematicians and geophysicists working with this theory.