A characterization of the inverse gravimetric source problem through extremal measures

Abstract

Most problems in applications are inverse source problems or identification problems. This review deals with a systematic treatment of the nonnegative sources (measures) relative to the Laplace equation and the heat conduction equation producing the same potential outside a domain • C R 3. This set is convex and weakly compact. Therefore the basic theorems on convex sets can be applied to such problems. Sets of extremal measures are characterized by geometric conditions. Almost nothing is known about the structure of the sources which produce the earth's gravitational field. Therefore these investigations may be of interest for the inverse problem in gravimetry. The following question remains unanswered in this review: to find additional conditions to select uniquely a measure producing the earth's gravitational field. This question is unanswered in most inverse source problems.

A unified approach to various techniques for the non-uniqueness of the inverse gravimetric problem and wavelet-based methods

“…This ansatz leads to a system of linear equations of which the minimal energy solution is chosen. A measure theoretic approach is discussed in [3,4,49]. Note that [3] also contains a list of references on historical remarks regarding the inverse gravimetric problem.…”

“…A measure theoretic approach is discussed in [3,4,49]. Note that [3] also contains a list of references on historical remarks regarding the inverse gravimetric problem. An interesting idea is to use the boundedness of the density 0 ≤ D ≤ D max given by physical considerations.…”

Low Temperature Fourier Transform Infrared Spectroscopic Studies of Hydrogenated Amorphous Silicon Nitride Films

“…A measure theoretic approach is discussed in [3,4,49]. Note that [3] also contains a list of references on historical remarks regarding the inverse gravimetric problem.…”

“…Note that [3] also contains a list of references on historical remarks regarding the inverse gravimetric problem.…”

“…Actually, the inverse gravimetric problem discussed here violates all three of Hadamard's criteria for a well-posed problem. 3 Currently at DAMTP.…”