Uniqueness for an inverse problem originating from magnetohydrodynamics. A class of smooth domains

Elena Beretta, Sergio Vessella

Research output: Contribution to journalArticle

Abstract

We consider the homogeneous Dirichlet problem Δu = - f(u) ≤ 0 in Ω with u = 0 on ∂Ω. We are interested in the inverse problem of determining the nonlinear source f from knowledge of the normal derivative of u, ∂u/∂n, on an open arc Γ of ∂Ω. It is well known that this fails if Ω is a ball. On the other hand, Beretta and Vogelius proved that an analytic source f is uniquely determined from knowledge of (∂u/∂n)Γ if Γ has at least a true corner. In this paper we try to bridge the gap finding a class of smooth domains for which the determination of analytic f is possible.

Original languageEnglish (US)
Pages (from-to)267-283
Number of pages17
JournalRoyal Society of Edinburgh - Proceedings A
Volume135
Issue number2
Publication statusPublished - Jan 1 2005

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ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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