# The Bilaplacian with Robin boundary conditions

@inproceedings{Buoso2021TheBW, title={The Bilaplacian with Robin boundary conditions}, author={Davide Buoso and James B. Kennedy}, year={2021} }

We introduce Robin boundary conditions for biharmonic operators, which are a model for elastically supported plates and are closely related to the study of spaces of traces of Sobolev functions. We study the dependence of the operator, its eigenvalues, and eigenfunctions on the Robin parameters. We show in particular that when the parameters go to plus infinity the Robin problem converges to other biharmonic problems, and obtain estimates on the rate of divergence when the parameters go to… Expand

#### 4 Citations

Two inequalities for the first Robin eigenvalue of the Finsler Laplacian

- Mathematics
- 2021

Abstract. Let Ω Ă R, n ě 2, be a bounded connected, open set with Lipschitz boundary. Let F be a suitable norm in R and let ∆Fu “ div pFξp∇uqF p∇uqq be the so-colled Finsler Laplacian, with u P HpΩq.… Expand

Semiclassical bounds for spectra of biharmonic operators.

- Mathematics
- 2019

The averaged variational principle (AVP) is applied to various biharmonic operators. For the Riesz mean $R_1(z)$ of the eigenvalues we improve the known sharp semiclassical bounds in terms of the… Expand

Positivity for the clamped plate equation under high tension

- Mathematics
- 2021

In this article we consider positivity issues for the clamped plate equation with high tension γ > 0. This equation is given by ∆2u − γ∆u = f under clamped boundary conditions. Here we show, that… Expand

A Sharp Isoperimetric Inequality for the Second Eigenvalue of the Robin Plate

- Mathematics
- 2020

Among all $C^{\infty}$ bounded domains with equal volume, we show that the second eigenvalue of the Robin plate is uniquely maximized by an open ball, so long as the Robin parameter lies within a… Expand

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