Geophysical Journal | 2009 volume 31 6

Alexidze problem for renovation of gravitation force potential

© Yu.I. Dubovenko

A new nonlinear gravimetric boundary problem, namely an Alexidze problem is stated. It is treated by Á. Chornii as a problem of gravity potential renovation by the values of modulus of its gradients given on Liapunov's boundary. The problem's analytical properties are considered. Its solution as a simple layer potential consists of the sequence of solutions of external boundary Neumann's problems for Laplace's equation provided that the solution does not greatly deviate from the given one. A simple layer density is defined by the solution of the 2-nd kind Fredholm integral equation for the gravity.

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