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In this work we prove the generic simplicity of the spectrum of the clamped plate equation in a bounded regular domain of R d. That is, given Ω ⊂ R d , we show that there exists an arbitrarily small deformation of the domain u, such that all the eigenvalues of the plate system in the deformed domain Ω + u are simple. To prove this result we first prove a… (More)

- J. H. ORTEGA
- 2001

In this work, we study an approximate control problem for the heat equation, with a nonstandard but rather natural restriction on the solution. It is well known that approximate controllability holds. On the other hand, the total mass of the solutions of the uncontrolled system is constant in time. Therefore, it is natural to analyze whether approximate… (More)

Our research aims at image segmentation using the variational framework of Mumford and Shah, following an approximation proposed by Ambrosio and Tortorelli. This technique circumvents the use of parametric contours and implicit level-set techniques, where its solution may be regarded as a soft seg-mentation, with a number the levels or colors being 2 N. On… (More)

- Grégoire Allaire, Carlos Conca, Luis Friz, Jaime H. Ortega, Bernard Dacorogna
- 2006

In this work, we study the Bloch wave decomposition for the Stokes equations in a periodic media in R d. We prove that, because of the incompress-ibility constraint, the Bloch eigenvalues, as functions of the Bloch frequency ξ, are not continuous at the origin. Nevertheless, when ξ goes to zero in a fixed direction, we exhibit a new limit spectral problem… (More)

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