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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)
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 segmentation, with a number the levels or colors being(More)
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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