Optimal exponentials of thickness in Korn’s inequalities for parabolic and elliptic shells

被引：0
作者：
Peng-Fei Yao
机构：
[1] Chinese Academy of Sciences,Key Laboratory of Systems and Control Institute of Systems Science, Academy of Mathematics and Systems Science
[2] University of Chinese Academy of Sciences,School of Mathematical Sciences
来源：
Annali di Matematica Pura ed Applicata (1923 -) | 2021年 / 200卷
关键词：
Korn’s inequality; Shell; Nonlinear elasticity; Riemannian geometry; 74K20 (primary); 74B20 (secondary);
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We consider the scaling of the optimal constant in Korn’s first inequality for elliptic and parabolic shells which was first given by Grabovsky and Harutyunyan with hints coming from the test functions constructed by Tovstik and Smirnov on the level of formal asymptotic expansions. Here, we employ the Bochner technique in Remannian geometry to remove the assumption that the middle surface of the shell is given by one single principal coordinate, in particularly, including closed elliptic shells.
引用
收藏
页码：379 / 401
页数：22
相关论文
共 47 条
  • [1] Korn A(1908)Solution gnrale du problme dquilibre dans la thorie de llasticit dans le cas o les erts sont donns la surface Ann. Fac. Sci. Toulouse 10 165-269
  • [2] Friedrichs KO(1947)On the boundary-value problems of the theory of elasticity and Korns inequality Ann. Math. 48 441-471
  • [3] Kondratiev VA(1988)Boundary value problems for a system in elasticity theory in unbounded domains. Korn inequalities Usp. Mat. Nauk 43 55-98
  • [4] Oleinik OA(1989)On Korns inequalities C. R. Math. Acad. Sci. Paris Ser. I 308 483-487
  • [5] Kondratiev VA(1982)New integral estimates for deformations in terms of their nonlinear strains Arch. Ration. Mech. Anal. 78 131-172
  • [6] Oleinik OA(1961)On Korns inequality Arch. Ration. Mech. Anal. 8 89-98
  • [7] Kohn RV(2013)Some Poincar type inequalities for quadratic matrix fields Proc. Appl. Math. Mech. 13 359-360
  • [8] Payne LE(2014)Korns second inequality and geometric rigidity with mixed growth conditions Calc. Var. Part. Differ. Equ. 50 437-454
  • [9] Weinberger HF(2011)A canonical extension of Korns first inequality to H(Curl) motivated by gradient plasticity with plastic spin C. R. Math. Acad. Sci. Paris Ser. I 349 1251-1254
  • [10] Bauer S(2002)A theorem on geometric rigidity and the derivation of nonlinear plate theory from three dimensional elasticity Commun. Pure Appl. Math. 55 1461-1506
12345