Isoperimetric Inequalities for Extremal Sobolev Functions

被引：0

作者：

Ratzkin, Jesse ^{[1
]}

Carroll, Tom ^{[2
]}

机构：

[1] Univ Cape Town, Dept Math & Appl Math, Cape Town, South Africa

[2] Univ Coll Cork, Sch Math Sci, Cork, Ireland

来源：

Extended Abstracts Fall 2013: Geometrical Analysis; Type Theory, Homotopy Theory and Univalent Foundations | 2015年

关键词：

EIGENFUNCTION; EIGENVALUES; MEMBRANE;

D O I：

10.1007/978-3-319-21284-5_13

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let be a bounded domain with boundary of class. One can measure various geometric and physical quantities attached to, such as volume, perimeter, diameter, in-radius, torsional rigidity, and principal frequency. The first chapter of [16] contains a long list of such interesting quantities, as well as their values for standard shapes such as disks, rectangles, strips, and triangles. © 2015 Springer International Publishing Switzerland.

引用

页码：67 / 71

页数：5

共 50 条

[1] Extremal functions for the anisotropic Sobolev inequalities
El Hamidi, A.
Rakotoson, J. M.
[J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2007, 24 (05): : 741 - 756
[2] A NOTE ON EXTREMAL FUNCTIONS FOR SHARP SOBOLEV INEQUALITIES
Barbosa, Ezequiel R.
Montenegro, Marcos
[J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2007,
[3] Extremal functions for optimal Sobolev inequalities on compact manifolds
Zindine Djadli
Olivier Druet
[J]. Calculus of Variations and Partial Differential Equations, 2001, 12 : 59 - 84
[4] Extremal functions for optimal Sobolev inequalities on compact manifolds
Djadli, Z
Druet, O
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2001, 12 (01) : 59 - 84
[5] Extremal functions in Poincare-Sobolev inequalities for functions of bounded variation
Bouchez, Vincent
Van Schaftingen, Jean
[J]. NONLINEAR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS, 2011, 540 : 47 - 58
[6] The existence of extremal functions for discrete Sobolev inequalities on lattice graphs
Hua, Bobo
Li, Ruowei
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 305 : 224 - 241
[7] Sobolev and isoperimetric inequalities with monomial weights
Cabre, Xavier
Ros-Oton, Xavier
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 255 (11) : 4312 - 4336
[8] SOBOLEV AND ISOPERIMETRIC INEQUALITIES FOR RIEMANNIAN SUBMANIFOLDS
HOFFMAN, D
SPRUCK, J
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1974, 27 (06) : 715 - 727
[9] Two isoperimetric inequalities for the Sobolev constant
Carroll, Tom
Ratzkin, Jesse
[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2012, 63 (05): : 855 - 863
[10] Two isoperimetric inequalities for the Sobolev constant
Tom Carroll
Jesse Ratzkin
[J]. Zeitschrift für angewandte Mathematik und Physik, 2012, 63 : 855 - 863

← 1 2 3 4 5 →