On the eigenvalues of the biharmonic operator with Neumann boundary conditions on a thin set

Francesco Ferraresso; Luigi Provenzano

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arXiv · 2108.03969

On the eigenvalues of the biharmonic operator with Neumann boundary conditions on a thin set

Francesco Ferraresso·Luigi Provenzano

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Abstract

Let $\Omega$ be a bounded domain in $\mathbb R^2$ with smooth boundary $\partial\Omega$, and let $\omega_h$ be the set of points in $\Omega$ whose distance from the boundary is smaller than $h$. We prove that the eigenvalues of the biharmonic operator on $\omega_h$ with Neumann boundary conditions converge to the eigenvalues of a limiting problem in the form of system of differential equations on $\partial\Omega$.

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Francesco Ferraresso, Luigi Provenzano. 2021-08-09. On the eigenvalues of the biharmonic operator with Neumann boundary conditions on a thin set. https://arxiv.org/abs/2108.03969

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