On the Eigenvalues of the Biharmonic Steklov Problem on a Thin Set
Abstract
This paper investigates the asymptotic behavior of the eigenvalues of the biharmonic operator on a thin set with Steklov boundary condition. The thin set is taken to be a tubular neighborhood of a planar smooth domain. We show that, as the thickness of this neighborhood tends to zero, all eigenvalues of the biharmonic operator with Steklov boundary condition converge to zero.
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