Displaying similar documents to “The squares of the Laplacian-Dirichlet eigenfunctions are generically linearly independent”

Some uniqueness and observability problems arising in the control of vibrations

Enrique Zuazua (1999)

Journées équations aux dérivées partielles

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We discuss a control problem for the Lamé system which naturally leads to the following uniqueness problem: Given a bounded domain of 𝐑 3 , are there non-trivial solutions of the evolution Lamé system with homogeneous Dirichlet boundary conditions for which the first two components vanish? We show that such solutions do not exist when the domain is Lipschitz. However, in two space dimensions one can build easily polygonal domains in which there are eigenvibrations with the first component...

Domain perturbations, capacity and shift of eigenvalues

André Noll (1999)

Journées équations aux dérivées partielles

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After introducing the notion of capacity in a general Hilbert space setting we look at the spectral bound of an arbitrary self-adjoint and semi-bounded operator H . If H is subjected to a domain perturbation the spectrum is shifted to the right. We show that the magnitude of this shift can be estimated in terms of the capacity. We improve the upper bound on the shift which was given in (, 24:759–775, 1999) and obtain a lower bound which leads to a generalization of Thirring’s inequality...

Spectrum of the laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions

David Krejčiřík (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the laplacian in a domain squeezed between two parallel curves in the plane, subject to Dirichlet boundary conditions on one of the curves and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the curves tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the curvature radii of the Neumann boundary to the Dirichlet...