A few shape optimization results for a biharmonic Steklov problem

Davide Buoso; Luigi Provenzano

doi:10.1016/j.jde.2015.03.013

A few shape optimization results for a biharmonic Steklov problem

Davide Buoso, Luigi Provenzano

Research output: Contribution to journal › Article › peer-review

Abstract

We derive the equation of a free vibrating thin plate whose mass is concentrated at the boundary, namely a Steklov problem for the biharmonic operator. We provide Hadamard-type formulas for the shape derivatives of the corresponding eigenvalues and prove that balls are critical domains under volume constraint. Finally, we prove an isoperimetric inequality for the first positive eigenvalue.

Original language	English
Pages (from-to)	1778-1818
Number of pages	41
Journal	Journal of Differential Equations
Volume	259
Issue number	5
DOIs	https://doi.org/10.1016/j.jde.2015.03.013
Publication status	Published - 5 Sept 2015
Externally published	Yes

Keywords

Biharmonic operator
Eigenvalues
Isoperimetric inequality
Isovolumetric perturbations
Steklov boundary conditions

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10.1016/j.jde.2015.03.013

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title = "A few shape optimization results for a biharmonic Steklov problem",

abstract = "We derive the equation of a free vibrating thin plate whose mass is concentrated at the boundary, namely a Steklov problem for the biharmonic operator. We provide Hadamard-type formulas for the shape derivatives of the corresponding eigenvalues and prove that balls are critical domains under volume constraint. Finally, we prove an isoperimetric inequality for the first positive eigenvalue.",

keywords = "Biharmonic operator, Eigenvalues, Isoperimetric inequality, Isovolumetric perturbations, Steklov boundary conditions",

author = "Davide Buoso and Luigi Provenzano",

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AU - Provenzano, Luigi

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N2 - We derive the equation of a free vibrating thin plate whose mass is concentrated at the boundary, namely a Steklov problem for the biharmonic operator. We provide Hadamard-type formulas for the shape derivatives of the corresponding eigenvalues and prove that balls are critical domains under volume constraint. Finally, we prove an isoperimetric inequality for the first positive eigenvalue.

AB - We derive the equation of a free vibrating thin plate whose mass is concentrated at the boundary, namely a Steklov problem for the biharmonic operator. We provide Hadamard-type formulas for the shape derivatives of the corresponding eigenvalues and prove that balls are critical domains under volume constraint. Finally, we prove an isoperimetric inequality for the first positive eigenvalue.

KW - Biharmonic operator

KW - Eigenvalues

KW - Isoperimetric inequality

KW - Isovolumetric perturbations

KW - Steklov boundary conditions

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DO - 10.1016/j.jde.2015.03.013

M3 - Article

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VL - 259

SP - 1778

EP - 1818

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 5

ER -

A few shape optimization results for a biharmonic Steklov problem

Abstract

Keywords

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