Justin L. Taylor
Published 2010-10-11, updated 2012-07-26Version 4
We consider the eigenvalues of an elliptic operator for systems with bounded, measurable, and symmetric coefficients. We assume we have two non-empty, open, disjoint, and bounded sets and add a set of small measure to form the perturbed domain. Then we show that the Dirichlet eigenvalues corresponding to the family of perturbed domains converge to the Dirichlet eigenvalues corresponding to the unperturbed domain. Moreover, our rate of convergence is independent of the eigenvalues. In this paper, we consider the Lam\'{e} system, systems which satisfy a strong ellipticity condition, and systems which satisfy a Legendre-Hadamard ellipticity condition.
On the convergence of statistical solutions of the 3D Navier-Stokes-$α$ model as $α$ vanishes
Convergence of approximate deconvolution models to the filtered Navier-Stokes Equations
Convergence of the self-dual Ginzburg-Landau gradient flow
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