On the first eigenvalue of a fourth order Steklov problem

Dorin Bucur; Alberto Ferrero; Filippo Gazzola

doi:10.1007/s00526-008-0199-9

On the first eigenvalue of a fourth order Steklov problem

Dorin Bucur
, Alberto Ferrero
, Filippo Gazzola

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

Abstract

We prove some results about the first Steklov eigenvalue d ₁ of the biharmonic operator in bounded domains. Firstly, we show that Fichera's principle of duality (Fichera in Atti Accad Naz Lincei 19:411-418, 1955) may be extended to a wide class of nonsmooth domains. Next, we study the optimization of d ₁ for varying domains: we disprove a long-standing conjecture, we show some new and unexpected features and we suggest some challenging problems. Finally, we prove several properties of the ball.

Original language	English
Pages (from-to)	103-131
Number of pages	29
Journal	Calculus of Variations and Partial Differential Equations
Volume	35
Issue number	1
DOIs	https://doi.org/10.1007/s00526-008-0199-9
Publication status	Published - May 2009
Externally published	Yes

Access to Document

10.1007/s00526-008-0199-9

Cite this

@article{c58536cec1dc4a9e9e0637d918e4c56c,

title = "On the first eigenvalue of a fourth order Steklov problem",

abstract = "We prove some results about the first Steklov eigenvalue d 1 of the biharmonic operator in bounded domains. Firstly, we show that Fichera's principle of duality (Fichera in Atti Accad Naz Lincei 19:411-418, 1955) may be extended to a wide class of nonsmooth domains. Next, we study the optimization of d 1 for varying domains: we disprove a long-standing conjecture, we show some new and unexpected features and we suggest some challenging problems. Finally, we prove several properties of the ball.",

author = "Dorin Bucur and Alberto Ferrero and Filippo Gazzola",

year = "2009",

month = may,

doi = "10.1007/s00526-008-0199-9",

language = "English",

volume = "35",

pages = "103--131",

journal = "Calculus of Variations and Partial Differential Equations",

issn = "0944-2669",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - On the first eigenvalue of a fourth order Steklov problem

AU - Bucur, Dorin

AU - Ferrero, Alberto

AU - Gazzola, Filippo

PY - 2009/5

Y1 - 2009/5

N2 - We prove some results about the first Steklov eigenvalue d 1 of the biharmonic operator in bounded domains. Firstly, we show that Fichera's principle of duality (Fichera in Atti Accad Naz Lincei 19:411-418, 1955) may be extended to a wide class of nonsmooth domains. Next, we study the optimization of d 1 for varying domains: we disprove a long-standing conjecture, we show some new and unexpected features and we suggest some challenging problems. Finally, we prove several properties of the ball.

AB - We prove some results about the first Steklov eigenvalue d 1 of the biharmonic operator in bounded domains. Firstly, we show that Fichera's principle of duality (Fichera in Atti Accad Naz Lincei 19:411-418, 1955) may be extended to a wide class of nonsmooth domains. Next, we study the optimization of d 1 for varying domains: we disprove a long-standing conjecture, we show some new and unexpected features and we suggest some challenging problems. Finally, we prove several properties of the ball.

UR - https://www.scopus.com/pages/publications/59349117132

U2 - 10.1007/s00526-008-0199-9

DO - 10.1007/s00526-008-0199-9

M3 - Article

SN - 0944-2669

VL - 35

SP - 103

EP - 131

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 1

ER -

On the first eigenvalue of a fourth order Steklov problem

Abstract

Access to Document

Other files and links

Fingerprint

Cite this