A relaxation result in the framework of structured deformations in a bounded variation setting

被引：9

作者：

Baia, Margarida ^{[1
]}

Matias, Jose ^{[1
]}

Santos, Pedro Miguel ^{[1
]}

机构：

[1] CAMGSD, Dept Matemat, Inst Super Tecn, P-1049001 Lisbon, Portugal

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2012年 / 142卷 / 02期

关键词：

GLOBAL METHOD; ENERGY; BULK; FUNCTIONALS; INTEGRANDS; THEOREM;

D O I：

10.1017/S0308210510001460

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain an integral representation of an energy for structured deformations of continua in the space of functions of bounded variation, as a first step to the study of asymptotic models for thin defective crystalline structures, where phenomena as slips, vacancies and dislocations prevent the effectiveness of classical theories.

引用

页码：239 / 271

页数：33

共 24 条

[1] A Dimension Reduction Result in the Framework of Structured Deformations
José Matias
Pedro Miguel Santos
[J]. Applied Mathematics & Optimization, 2014, 69 : 459 - 485
[2] A Dimension Reduction Result in the Framework of Structured Deformations
Matias, Jose
Santos, Pedro Miguel
[J]. APPLIED MATHEMATICS AND OPTIMIZATION, 2014, 69 (03): : 459 - 485
[3] Second-Order Structured Deformations in the Space of Functions of Bounded Hessian
Irene Fonseca
Adrian Hagerty
Roberto Paroni
[J]. Journal of Nonlinear Science, 2019, 29 : 2699 - 2734
[4] Second-Order Structured Deformations in the Space of Functions of Bounded Hessian
Fonseca, Irene
Hagerty, Adrian
Paroni, Roberto
[J]. JOURNAL OF NONLINEAR SCIENCE, 2019, 29 (06) : 2699 - 2734
[5] A BURENKOV'S TYPE RESULT FOR FUNCTIONS OF BOUNDED κ-VARIATION
Gimenez, Jose
Lopez, Lorena
Merentes, Nelson
Sanchez, J. L.
[J]. ANNALS OF FUNCTIONAL ANALYSIS, 2015, 6 (01): : 1 - 11
[6] A global method for relaxation for multi-levelled structured deformations
Barroso, Ana Cristina
Matias, Jose
Zappale, Elvira
[J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2024, 31 (04):
[7] Second-Order Structured Deformations: Relaxation, Integral Representation and Applications
Barroso, Ana Cristina
Matias, Jose
Morandotti, Marco
Owen, David R.
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2017, 225 (03) : 1025 - 1072
[8] Second-Order Structured Deformations: Relaxation, Integral Representation and Applications
Ana Cristina Barroso
José Matias
Marco Morandotti
David R. Owen
[J]. Archive for Rational Mechanics and Analysis, 2017, 225 : 1025 - 1072
[9] MINIMAL CURRENTS AND RELAXATION OF VARIATIONAL INTEGRALS ON MAPPINGS OF BOUNDED VARIATION
AVILES, P
GIGA, Y
[J]. PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1990, 66 (03) : 68 - 71
[10] A Relaxation Result in the Vectorial Setting and Power Law Approximation for Supremal Functionals
Francesca Prinari
Elvira Zappale
[J]. Journal of Optimization Theory and Applications, 2020, 186 : 412 - 452

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