Recovery of potential using module values of its gradient. 2
DOI:
https://doi.org/10.24028/gzh.0203-3100.v22i6.2000.214576Abstract
The method of the recovery of the potential on the module of its gradient under conditionof the similarity of the potential to that given as the limit of the succession of the solations of the boundary problems of Neumann for the Laplace equation that define the disturbing potential proposed in the first part is substantiated. The succession of the disturbing potential is generated by the succession of the solutions of linear integral equations of the second kind with compact operators having large cores. A correct solubility of the given kind of equations is established and the convergence of the succession of the solution of the Neumann's problems to the function unambiguously generating the desired potential is proven.
References
Черный А. В., Якимчик А. И. Восстановление потенциала по значениям модуля его градиента. 1 // Геофиз. журн. — 1999. — 21, № 3. — С. 55—72.
Владимиров В. С. Уравнения математической физики. — М.: Наука, 1971. — 512 с.
Канторович Л. В., Акилов Г. П. Функциональный анализ. — М.: Наука, 1977. — 744 с.
Рис Ф., Секефальви-Надь Б. Лекции по функциональному анализу. — М.: Мир, 1979. — 592 с.
Михлин С. Г. Лекции по линейным интегральным уравнениям. — М.: Физматгиз, 1959. —232 с.
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