Analyticity and criticality results for the eigenvalues of the biharmonic operator

Davide Buoso

doi:10.1007/978-3-319-41538-3_5

Analyticity and criticality results for the eigenvalues of the biharmonic operator

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov).We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove that balls are always critical domains under volume constraint.

Original language	English
Title of host publication	Geometric Properties for Parabolic and Elliptic PDE’s - GPPEPDEs 2015
Editors	Carlo Nitsch, Filippo Gazzola, Kazuhiro Ishige, Paolo Salani
Publisher	Springer New York LLC
Pages	65-85
Number of pages	21
ISBN (Print)	9783319415369
DOIs	https://doi.org/10.1007/978-3-319-41538-3_5
Publication status	Published - 2016
Externally published	Yes
Event	Italian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDE’s, GPPEPDEs 2015 - Palinuro, Italy Duration: 25 May 2015 → 29 May 2015

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	176
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	Italian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDE’s, GPPEPDEs 2015
Country/Territory	Italy
City	Palinuro
Period	25/05/15 → 29/05/15

Keywords

Biharmonic operator
Boundary value problems
Eigenvalues
Hadamard formulas
Isovolumetric perturbations
Perturbations
Plates
Shape criticality
Steklov

Access to Document

10.1007/978-3-319-41538-3_5

Cite this

Buoso, D. (2016). Analyticity and criticality results for the eigenvalues of the biharmonic operator. In C. Nitsch, F. Gazzola, K. Ishige, & P. Salani (Eds.), Geometric Properties for Parabolic and Elliptic PDE’s - GPPEPDEs 2015 (pp. 65-85). (Springer Proceedings in Mathematics and Statistics; Vol. 176). Springer New York LLC. https://doi.org/10.1007/978-3-319-41538-3_5

@inproceedings{c0249901834042278b3a9f2bbe4ec5c4,

title = "Analyticity and criticality results for the eigenvalues of the biharmonic operator",

abstract = "We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov).We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove that balls are always critical domains under volume constraint.",

keywords = "Biharmonic operator, Boundary value problems, Eigenvalues, Hadamard formulas, Isovolumetric perturbations, Perturbations, Plates, Shape criticality, Steklov",

author = "Davide Buoso",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2016.; Italian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDE{\textquoteright}s, GPPEPDEs 2015 ; Conference date: 25-05-2015 Through 29-05-2015",

year = "2016",

doi = "10.1007/978-3-319-41538-3_5",

language = "English",

isbn = "9783319415369",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer New York LLC",

pages = "65--85",

editor = "Carlo Nitsch and Filippo Gazzola and Kazuhiro Ishige and Paolo Salani",

booktitle = "Geometric Properties for Parabolic and Elliptic PDE{\textquoteright}s - GPPEPDEs 2015",

}

Buoso, D 2016, Analyticity and criticality results for the eigenvalues of the biharmonic operator. in C Nitsch, F Gazzola, K Ishige & P Salani (eds), Geometric Properties for Parabolic and Elliptic PDE’s - GPPEPDEs 2015. Springer Proceedings in Mathematics and Statistics, vol. 176, Springer New York LLC, pp. 65-85, Italian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDE’s, GPPEPDEs 2015, Palinuro, Italy, 25/05/15. https://doi.org/10.1007/978-3-319-41538-3_5

Analyticity and criticality results for the eigenvalues of the biharmonic operator. / Buoso, Davide.
Geometric Properties for Parabolic and Elliptic PDE’s - GPPEPDEs 2015. ed. / Carlo Nitsch; Filippo Gazzola; Kazuhiro Ishige; Paolo Salani. Springer New York LLC, 2016. p. 65-85 (Springer Proceedings in Mathematics and Statistics; Vol. 176).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Analyticity and criticality results for the eigenvalues of the biharmonic operator

AU - Buoso, Davide

N1 - Publisher Copyright: © Springer International Publishing Switzerland 2016.

PY - 2016

Y1 - 2016

N2 - We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov).We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove that balls are always critical domains under volume constraint.

AB - We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov).We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove that balls are always critical domains under volume constraint.

KW - Biharmonic operator

KW - Boundary value problems

KW - Eigenvalues

KW - Hadamard formulas

KW - Isovolumetric perturbations

KW - Perturbations

KW - Plates

KW - Shape criticality

KW - Steklov

UR - http://www.scopus.com/inward/record.url?scp=84985041023&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-41538-3_5

DO - 10.1007/978-3-319-41538-3_5

M3 - Conference contribution

AN - SCOPUS:84985041023

SN - 9783319415369

T3 - Springer Proceedings in Mathematics and Statistics

SP - 65

EP - 85

BT - Geometric Properties for Parabolic and Elliptic PDE’s - GPPEPDEs 2015

A2 - Nitsch, Carlo

A2 - Gazzola, Filippo

A2 - Ishige, Kazuhiro

A2 - Salani, Paolo

PB - Springer New York LLC

T2 - Italian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDE’s, GPPEPDEs 2015

Y2 - 25 May 2015 through 29 May 2015

ER -

Analyticity and criticality results for the eigenvalues of the biharmonic operator

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Cite this