ON TWO FUNCTIONALS INVOLVING THE MAXIMUM OF THE TORSION FUNCTION

被引：14

作者：

Henrot, Antoine ^{[1
]}

Lucardesi, Ilaria ^{[1
]}

Philippin, Gerard ^{[2
]}

机构：

[1] Univ Lorraine, Inst Elie Cartan Lorraine, CNRS, UMR 7502, Vandoeuvre Les Nancy, France

[2] Univ Laval Quebec, Dept Math, Quebec City, PQ G1V 0A6, Canada

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2018年 / 24卷 / 04期

关键词：

Torsional rigidity; first Dirichlet eigenvalue; shape optimization; INEQUALITY; DOMAINS;

D O I：

10.1051/cocv/2017069

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper we investigate upper and lower bounds of two shape functionals involving the maximum of the torsion function. More precisely, we consider T(Omega)/(M(Omega)vertical bar Omega vertical bar) and M(Omega)lambda(1)(Omega), where Omega is a bounded open set of R-d with finite Lebesgue measure vertical bar Omega vertical bar, M(Omega) denotes the maximum of the torsion function, T(Omega) the torsion, and lambda(1)(Omega) the first Dirichlet eigenvalue. Particular attention is devoted to the subclass of convex sets.

引用

页码：1585 / 1604

页数：20

共 29 条

[1]

[Anonymous], SOME ASPECTS MECH 1

[2] Solutions of the Cheeger problem via torsion functions [J].

Bueno, H. ;

Ercole, G. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 381 (01) :263-279

[3]

Buttazzo G., 2005, PROGR NONLIN DIFFER

[4]

Cioranescu D., 1997, PROGR NONLINEAR DIFF, V31, P45

[5]

Della Pietra F., 2017, ARXIV170503330

[6] APPROXIMATION OF DIRICHLET EIGENVALUES ON DOMAINS WITH SMALL HOLES [J].

FLUCHER, M .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1995, 193 (01) :169-199

[7]

Henrot A, 2005, MATH APPL-BERLIN, V48, P1

[8]

Henrot A, 2006, FRONT MATH, P1

[9]

Kacimi H., 1989, Partial Differential Equations and the Calculus of Variations, V2, P661

[10] POWER CONCAVITY AND BOUNDARY-VALUE PROBLEMS [J].

KENNINGTON, AU .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1985, 34 (03) :687-704

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