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

Published online by Cambridge University Press:  12 July 2007

Elena Beretta
Affiliation:
Dipartimento di Matematica, Istituto ‘Guido Castelnuovo’, Università ‘La Sapienza’, Piazzale Aldo Moro 2, 00185 Roma, Italy
Sergio Vessella
Affiliation:
Dipartimento di Matematica (DiMaD), Università di Firenze, Via Lombroso 6/17, 50134 Firenze, Italy

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/δn, 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

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2005

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