Some asymptotic problems of linear elasticity. (English) Zbl 0651.73008
Material instabilities in continuum mechanics, Proc. Symp. Edinburgh/Scotl. 1985/86, 343-357 (1988).
[For the entire collection see Zbl 0627.00023.]
The paper deals with the asymptotic behavior at infinity of solutions of the linear elastic systems having finite energy integrals. To do this, some generalizations of Korn’s inequality are provided through several theorems and lemmas. The Dirichlet problem for a biharmonic equation is studied and the best estimates for weak solutions, under stipulated boundary conditions, are obtained and presented.
The paper deals with the asymptotic behavior at infinity of solutions of the linear elastic systems having finite energy integrals. To do this, some generalizations of Korn’s inequality are provided through several theorems and lemmas. The Dirichlet problem for a biharmonic equation is studied and the best estimates for weak solutions, under stipulated boundary conditions, are obtained and presented.
Reviewer: V.K.Arya
MSC:
| 74B99 | Elastic materials |
| 74B05 | Classical linear elasticity |
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 49J45 | Methods involving semicontinuity and convergence; relaxation |
| 31B30 | Biharmonic and polyharmonic equations and functions in higher dimensions |
| 31B20 | Boundary value and inverse problems for harmonic functions in higher dimensions |
