EIGENVALUES OF POLYHARMONIC OPERATORS ON VARIABLE DOMAINS

被引：32

作者：

Buoso, Davide ^{[1
]}

Lamberti, Pier Domenico ^{[1
]}

机构：

[1] Univ Padua, Dipartimento Matemat, I-35126 Padua, Italy

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2013年 / 19卷 / 04期

关键词：

Polyharmonic operators; eigenvalues; domain perturbation; RAYLEIGHS CONJECTURE; SPECTRAL STABILITY; LAPLACE OPERATOR; PERTURBATION;

D O I：

10.1051/cocv/2013054

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We consider a class of eigenvalue problems for polyharmonic operators, including Dirichlet and buckling-type eigenvalue problems. We prove an analyticity result for the dependence of the symmetric functions of the eigenvalues upon domain perturbations and compute Hadamard-type formulas for the Frechet differentials. We also consider isovolumetric domain perturbations and characterize the corresponding critical domains for the symmetric functions of the eigenvalues. Finally, we prove that balls are critical domains.

引用

页码：1225 / 1235

页数：11

共 29 条

[1]

Agmon S., 1965, VANNOSTRAND MATH STU, V2

[2]

[Anonymous], J MATH SCI NY

[3]

[Anonymous], LECT OB M QUAL PROP

[4]

[Anonymous], 2005, London Mathematical Society Lecture Note Series

[5]

[Anonymous], LECT NOTES MATH

[6]

[Anonymous], NOTES COURSES GIVEN

[7]

[Anonymous], TRABALHO MATH

[8]

[Anonymous], SIAM J CONTROL OPTIM

[9] On the isoperimetric inequality for the buckling of a clamped plate [J].

S. Ashbaugh ;

Dorin Bucur .

Zeitschrift für angewandte Mathematik und Physik ZAMP, 2003, 54 (5) :756-770

[10] ON RAYLEIGHS CONJECTURE FOR THE CLAMPED PLATE AND ITS GENERALIZATION TO 3 DIMENSIONS [J].

ASHBAUGH, MS ;

BENGURIA, RD .

DUKE MATHEMATICAL JOURNAL, 1995, 78 (01) :1-17

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