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Potential Analysis

, Volume 2, Issue 4, pp 387–400 | Cite as

Application du prolongement analytique au problème inverse du potentiel

  • Oleg Loukianov
Article
  • 24 Downloads

Sommaire

Le but de cet article est établir quelques résultats nouveaux sur le problème inverse du potentiel newtonien. Nous démontrons deux théorèmes d'unicité: pour les polyédres convexes dansR n et pour les lemniscates dansR2. L'instrument principal est un lemme basé sur une idée de V. Kondrachkov rarement utilisé malgré sa puissance. Nous montrons son efficacité en liaison avec la méthode du prolongement analytique des potentiels.

Abstract

The goal of this paper is to establish some new results in the inverse Newtonian potential problem. We prove two uniqueness theorems: for convex polyhedra inR n and for lemniscates inR2. The main tool is a lemma based upon an idea of V. Kondrashkov which, though powerful, is rarely used. We show its efficiency applied together with the method of analytic continuation of potentials.

Mathematics Subject Classifications (1991)

31A25 31B20 

Key words

Newtonian potential external inverse problem analytic continuation 

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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Oleg Loukianov
    • 1
  1. 1.Equipe d'Analyse et ProbabilitésUniversité d'Evry Val-d'EssonneEvry CédexFrance

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