ON TORSIONAL RIGIDITY AND PRINCIPAL FREQUENCIES: AN INVITATION TO THE KOHLER-JOBIN REARRANGEMENT TECHNIQUE

被引：34

作者：

Brasco, Lorenzo ^{[1
]}

机构：

[1] Aix Marseille Univ, Lab Anal, 39 Rue Frederic Joliot Curie, F-13453 Marseille 13, France

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2014年 / 20卷 / 02期

关键词：

Torsional rigidity; nonlinear eigenvalue problems; spherical rearrangements; CONVEX SYMMETRIZATION; EXTREMAL-FUNCTIONS; REGULARITY;

D O I：

10.1051/cocv/2013065

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 generalize to the p-Laplacian. Delta(p) a spectral inequality proved by M.-T. Kohler-Jobin. As a particular case of such a generalization, we obtain a sharp lower bound on the first Dirichlet eigenvalue of Delta(p) of a set in terms of its p-torsional rigidity. The result is valid in every space dimension, for every 1 < p < infinity and for every open set with finite measure. Moreover, it holds by replacing the first eigenvalue with more general optimal Poincare-Sobolev constants. The method of proof is based on a generalization of the rearrangement technique introduced by Kohler-Jobin.

引用

页码：315 / 338

页数：24

共 26 条

[1] Convex symmetrization and applications [J].

Alvino, A ;

Ferone, V ;

Trombetti, G ;

Lions, PL .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1997, 14 (02) :275-293

[2]

Ambrosio L., 2004, Oxford Lecture Ser. Math. Appl., V25

[3]

[Anonymous], J MATH MECH

[4]

[Anonymous], FRONTIERS IN MATHEMA

[5]

[Anonymous], PREPRINT

[6] The pseudo-p-Laplace eigenvalue problem and viscosity solutions as p→∞ [J].

Belloni, M ;

Kawohl, B .

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2004, 10 (01) :28-52

[7]

Bucur D., 2005, Prog. Nonlinear Differ. Equ. Appl, V65

[8] Interpolating between torsional rigidity and principal frequency [J].

Carroll, Tom ;

Ratzkin, Jesse .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 379 (02) :818-826

[9] C1+ALPHA LOCAL REGULARITY OF WEAK SOLUTIONS OF DEGENERATE ELLIPTIC-EQUATIONS [J].

DIBENEDETTO, E .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1983, 7 (08) :827-850

[10] Convex symmetrization and Polya-Szego inequality [J].

Esposito, L ;

Trombetti, C .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2004, 56 (01) :43-62

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