On Problems in the Calculus of Variations in Increasingly Elongated Domains

被引：2

作者：

Le Dret, Herve ^{[1
]}

Mokrane, Amira ^{[2
,3
]}

机构：

[1] UPMC Univ Paris 06, Sorbonne Univ, CNRS, Lab Jacques Louis Liona, Boite Courrier 187, F-75252 Paris 05, France

[2] ENS, Lab Equat Derivees Partielles Non Lineaires & His, BP 92, Algiers 16050, Algeria

[3] USTHB, Fac Math, Dept Analyse, Lab Analyse Math & Numer Equat Derivees Partielle, Bab Ezzouar, Alger, Algeria

来源：

CHINESE ANNALS OF MATHEMATICS SERIES B | 2018年 / 39卷 / 02期

关键词：

Calculus of variations; Domains becoming unbounded; Asymptotic behavior; Exponential rate of convergence; ASYMPTOTIC-BEHAVIOR; CYLINDRICAL DOMAINS; QUASICONVEXITY; ELASTICITY;

D O I：

10.1007/s11401-018-1058-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper deals with minimization problems 41 the calculus of variations set in a sequence of domains, the size of which tends to infinity in certain directions and such that the data only depend on the coordinates in the directions that remain constant. The authors study the asymptotic behavior of minimizers in various situations and show that they converge in an appropriate sense toward minimizers of a related energy functional in the constant directions.

引用

页码：163 / 182

页数：20

共 18 条

[11] ON SOME VARIATIONAL PROBLEMS SET ON DOMAINS TENDING TO INFINITY
Chipot, Michel
Mojsic, Aleksandar
Roy, Prosenjit
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2016, 36 (07) : 3603 - 3621
[12] Dacorogna B., 2000, DIRECT METHODS CALCU
[13] EVANS LC, 1986, ARCH RATION MECH AN, V95, P227
[14] Juditsky A., 2014, Stochastic Systems, V4, P44
[15] LeDret H, 1995, J MATH PURE APPL, V74, P549
[16] NORMAL HYPERBOLICITY OF CENTER MANIFOLDS AND SAINTVENANT PRINCIPLE
MIELKE, A
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1990, 110 (04) : 353 - 372
[17] Toupin R. A., 1965, Arch. Ration. Mech. Anal., V18, P83, DOI [10.1007/BF00282253, DOI 10.1007/BF00282253]
[18] Xie Y., 2006, THESIS

← 1 2 →