Pedro Gómez Venegas and Ramón Mendoza 2006 Inverse Problems 22 1575 doi:10.1088/0266-5611/22/5/004
Uniqueness for the Dirichlet–Neumann elliptic functional
Pedro Gómez Venegas1 and Ramón Mendoza2
Show affiliationsIn this paper, we apply a well-known result on a conformal structure on a disc to prove the injectiveness of the Dirichlet–Neumann functional on the Riemannian metrics orbit space. The main result is that the only obstruction to injectiveness is the semidirect product of the groups of diffeomorphism that restricts to the identity on the boundary and the Abelian group of a real-valued function that restricts to zero on the boundary.
- PACS
- MSC
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58D05 Groups of diffeomorphisms and homeomorphisms as manifolds (See also 22E65, 57S05)
35A05 General existence and uniqueness theorems
35R30 Inverse problems (undetermined coefficients, etc.) for PDE
- Subjects
- Dates
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Issue 5 (October 2006)
Received 12 December 2005, in final form 2 May 2006
Published 24 July 2006
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Uniqueness for the Dirichlet–Neumann elliptic functional
Pedro Gómez Venegas and Ramón Mendoza 2006 Inverse Problems 22 1575
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