A Korn-Poincaré-type inequality for special functions of bounded deformation
作者： Manuel Friedrich
DOI:
关键词:
摘要: We present a Korn-Poincar\'e-type inequality in planar setting which is the spirit of Poincar\'e SBV due to De Giorgi, Carriero, Leaci. show that for each function SBD$^2$ one can find modification differs from original displacement field only on small set such distance suitable infinitesimal rigid motion be controlled by an appropriate combination elastic and surface energy. In particular, result used obtain compactness estimates functions bounded deformation.
arxiv.org
harvard.edu参考文章(24)
G. Dal Maso, M. Negri, D. Percivale, Linearized Elasticity as Γ-Limit of Finite Elasticity Set-valued Analysis. ,vol. 10, pp. 165- 183 ,(2002) , 10.1023/A:1016577431636
Diego Pallara, Luigi Ambrosio, Nicola Fusco, Functions of Bounded Variation and Free Discontinuity Problems ,(2000)
Roger Temam, Mathematical Problems in Plasticity ,(1985)
Franco Tomarelli, Antonio Leaci, Michele Carriero, About Poincaré Inequalities for Functions Lacking Summability Note di Matematica. ,vol. 31, pp. 67- 86 ,(2012) , 10.1285/I15900932V31N1P67
LawrenceCraig Evans, Measure theory and fine properties of functions ,(1992)
Manuel Friedrich, Bernd Schmidt, A quantitative geometric rigidity result in SBD arXiv: Analysis of PDEs. ,(2015)
Luigi Ambrosio, Alessandra Coscia, Gianni Dal Maso, Fine Properties of Functions with Bounded Deformation Archive for Rational Mechanics and Analysis. ,vol. 139, pp. 201- 238 ,(1997) , 10.1007/S002050050051
Antonin Chambolle, An approximation result for special functions with bounded deformation Journal de Mathématiques Pures et Appliquées. ,vol. 83, pp. 929- 954 ,(2004) , 10.1016/J.MATPUR.2004.02.004
Antonin Chambolle, A Density Result in Two-Dimensional Linearized Elasticity, and Applications Archive for Rational Mechanics and Analysis. ,vol. 167, pp. 211- 233 ,(2003) , 10.1007/S00205-002-0240-7
Bernd Schmidt, Fernando Fraternali, Michael Ortiz, Eigenfracture: An Eigendeformation Approach to Variational Fracture Multiscale Modeling & Simulation. ,vol. 7, pp. 1237- 1266 ,(2009) , 10.1137/080712568