A RELAXATION RESULT OF FUNCTIONALS IN THE SPACE SBD(Ω)

doi:10.1016/S0252-9602(08)60078-8

数学物理学报(英文版)

A RELAXATION RESULT OF FUNCTIONALS IN THE SPACE SBD(Ω)

吕中学; 杨孝平

徐州师范大学数学学院, 徐州 221116

收稿日期:2006-08-23 修回日期:1900-01-01 出版日期:2008-10-20 发布日期:2008-10-20
通讯作者: 杨孝平
基金资助:
This work is supported by the Doctorial Programme Foundation of Education
Ministry of of China (20030288002) and the Science Foundation of Jiangsu Province (BK2006209) and Natural Science Foundation of Jiangsu Higher Education Bureau (07KJD110206) and NNSF of China (10771181)

A RELAXATION RESULT OF FUNCTIONALS IN THE SPACE SBD(Ω)

Lü Zhongxue; Yang Xiaoping

School of Mathematical Science, Xuzhou Normal University, Xuzhou 221116, China; School of Sciences, Nanjing University of Science and Technology, Nanjing 210094, China

Received:2006-08-23 Revised:1900-01-01 Online:2008-10-20 Published:2008-10-20
Contact: Yang Xiaoping

摘要/Abstract

摘要：

In this article, the authors obtain an integral representation for the relaxation of the functional F(x, u, Ω):={∫Ω f(x, u(x), εu(x))dx if u ∈ W^{1, 1}(Ω, R^N), +∞ otherwise,
in the space of functions of bounded deformation, with respect to L¹-convergence. Here εu represents the absolutely continuous part of the symmetrized distributional derivative εu.f(x, p, ξ) satisfying weak convexity assumption.

关键词: Integral representation, relaxation, special functions with bounded deformation

Abstract:

In this article, the authors obtain an integral representation for the relaxation of the functional
F(x, u, Ω):={∫_Ωf(x, u(x), εu(x))dx if u ∈ W^{1, 1}(Ω, R^N), +∞ otherwise,
in the space of functions of bounded deformation, with respect to L¹-convergence. Here εu represents the absolutely continuous part of the symmetrized distributional derivative εu.f(x, p, ξ) satisfying weak convexity assumption.

Key words: Integral representation, relaxation, special functions with bounded deformation

中图分类号:

49J10

吕中学; 杨孝平. A RELAXATION RESULT OF FUNCTIONALS IN THE SPACE SBD(Ω)[J]. 数学物理学报(英文版), 2008, 28(4): 770-778.

Lü Zhongxue; Yang Xiaoping. A RELAXATION RESULT OF FUNCTIONALS IN THE SPACE SBD(Ω)[J]. Acta mathematica scientia,Series B, 2008, 28(4): 770-778.

[1]	Ozge AKCAY. THE REPRESENTATION OF THE SOLUTION OF STURM-LIOUVILLE EQUATION WITH DISCONTINUITY CONDITIONS[J]. 数学物理学报(英文版), 2018, 38(4): 1195-1213.
[2]	丁小丽, 蒋耀林. NONNEGATIVITY OF SOLUTIONS OF NONLINEAR FRACTIONAL DIFFERENTIAL-ALGEBRAIC EQUATIONS[J]. 数学物理学报(英文版), 2018, 38(3): 756-768.
[3]	吴舜堂. GENERAL DECAY OF SOLUTIONS FOR A VISCOELASTIC EQUATION WITH BALAKRISHNAN-TAYLOR DAMPING AND NONLINEAR BOUNDARY DAMPING-SOURCE INTERACTIONS[J]. 数学物理学报(英文版), 2015, 35(5): 981-994.
[4]	Corrado MASCIA. TWENTY-EIGHT YEARS WITH “HYPERBOLIC CONSERVATION LAWS WITH RELAXATION”[J]. 数学物理学报(英文版), 2015, 35(4): 807-831.
[5]	曹文涛, 黄飞敏. ON THE CONVERGENCE RATE OF A CLASS OF REACTION HYPERBOLIC SYSTEMS FOR AXONAL TRANSPORT[J]. 数学物理学报(英文版), 2015, 35(4): 945-954.
[6]	Sun Hye PARK. GENERAL DECAY OF A TRANSMISSION PROBLEM FOR KIRCHHOFF TYPE WAVE EQUATIONS WITH BOUNDARY MEMORY CONDITION[J]. 数学物理学报(英文版), 2014, 34(5): 1395-1403.
[7]	Jum-Ran KANG. GENERAL DECAY FOR A DIFFERENTIAL INCLUSION OF KIRCHHOFF TYPE WITH A MEMORY CONDITION AT THE BOUNDARY[J]. 数学物理学报(英文版), 2014, 34(3): 729-738.
[8]	N. TATAR. EXPONENTIAL DECAY FOR A VISCOELASTICALLY DAMPED TIMOSHENKO BEAM[J]. 数学物理学报(英文版), 2013, 33(2): 505-524.
[9]	陆云光, Christian Klingenberg. SINGULAR LIMITS FOR INHOMOGENEOUS EQUATIONS OF ELASTICITY[J]. 数学物理学报(英文版), 2009, 29(3): 645-649.
[10]	黎勇. RELAXATION TIME LIMITS PROBLEM FOR HYDRODYNAMIC MODELS IN #br# SEMICONDUCTOR SCIENCE[J]. 数学物理学报(英文版), 2007, 27(2): 437-448.
[11]	伍锦棠; 郑永树. SOME RESULTS ON HYPERBOLIC SYSTEMS WITH RELAXATION[J]. 数学物理学报(英文版), 2006, 26(4): 767-780.
[12]	何成, 李海梁. ASYMPTOTIC BEHAVIOR TOWARD THE RAREFACTION WAVE FOR SOLUTIONS OF RATE-TYPE VISCOELASTIC SYSTEM WITH BOUNDARY EFFECT[J]. 数学物理学报(英文版), 2000, 20(2): 245-255.
[13]	潘荣华. THE NONLINEAR STABILITY OF TRAVELLING WAVE SOLUTIONS FOR A REACTING FLOW MODEL WITH SOURCE TERM[J]. 数学物理学报(英文版), 1999, 19(1): 26-36.
[14]	项筱玲. OPTIMAL CONTROL OF A CLASS OF INFINTIE DIMENSIONAL UNCERTAIN SYSTEMS[J]. 数学物理学报(英文版), 1994, 14(S1): 78-87.

A RELAXATION RESULT OF FUNCTIONALS IN THE SPACE SBD(Ω)

A RELAXATION RESULT OF FUNCTIONALS IN THE SPACE SBD(Ω)

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 14

Metrics

本文评价

推荐阅读 0