### 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 language | English (US) |
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Pages (from-to) | 267-283 |

Number of pages | 17 |

Journal | Royal Society of Edinburgh - Proceedings A |

Volume | 135 |

Issue number | 2 |

State | Published - Jan 1 2005 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Royal Society of Edinburgh - Proceedings A*,

*135*(2), 267-283.

**Uniqueness for an inverse problem originating from magnetohydrodynamics. A class of smooth domains.** / Beretta, Elena; Vessella, Sergio.

Research output: Contribution to journal › Article

*Royal Society of Edinburgh - Proceedings A*, vol. 135, no. 2, pp. 267-283.

}

TY - JOUR

T1 - Uniqueness for an inverse problem originating from magnetohydrodynamics. A class of smooth domains

AU - Beretta, Elena

AU - Vessella, Sergio

PY - 2005/1/1

Y1 - 2005/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=17744388586&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=17744388586&partnerID=8YFLogxK

M3 - Article

VL - 135

SP - 267

EP - 283

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

SN - 0308-2105

IS - 2

ER -