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Fundamentalnaya i Prikladnaya Matematika, 1996, Volume 2, Issue 4, Pages 1195–1204
(Mi fpm182)
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This article is cited in 1 scientific paper (total in 1 paper)
Harmonic solution for the inverse problem of the Newtonian potential theory
J. Bosgiraud Université Paris VIII
Abstract:
We study from a theoretical point of view the Backus and Gilbert method in the case of Newtonian potential. If a mass distribution $m$ on a open set $\Omega$ creates a Newtonian potential $U^m$, which is known on an infinity of points $(y_n)_{n\in\mathbb N}$ out of $\overline{\Omega}$, we characterize the solution $m_0$, obtained as a generalization of the Backus and Gilbert method, as the projection of $m$ (for the scalar product of $L_2(\Omega)$) on a subspace of harmonic functions; this subspace may be the subspace of all harmonic, square-integrable functions (for example, if $\Omega$ is a starlike domain). Then we study the reproducing kernel $B$ associated to this projection, which satisfies
$$
m_0(x)=\int\limits_{\Omega}B(x,y)m(y)\,dy
$$
for any $m\in L_2(\Omega)$.
Received: 01.03.1995
Citation:
J. Bosgiraud, “Harmonic solution for the inverse problem of the Newtonian potential theory”, Fundam. Prikl. Mat., 2:4 (1996), 1195–1204
Linking options:
https://www.mathnet.ru/eng/fpm182 https://www.mathnet.ru/eng/fpm/v2/i4/p1195
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Abstract page: | 212 | Full-text PDF : | 86 | First page: | 2 |
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