Solvability on boundary-value problems of elasticity of three-dimensional quasicrystals

Weak solution (or generalized solution) for the boundary-value problems of partial differential equations of elasticity of 3D (three-dimensional) quasicrystals is given, in which the matrix expression is used. In terms of Korn inequality and theory of function space,we prove the uniqueness of the weak solution.This gives an extension of existence theorem of solution for classical elasticity to that of quasicrystals,and develops the weak solution theory of elasticity of 2D quasicrystals given by the second author of the paper and his students.     

准晶弹性理论边值问题的可解性

通过给出准晶弹性偏微分方程组边值问题的矩阵表示去定义弱解,利用Korn不等式和函数空间理论证明了这种弱解的存在性与唯一性,从而把经典弹性理论边值问题解的存在性定理推广到准晶弹性理论上,这种理论为发展极其复杂与困难的准晶弹性的偏微分方程的边值问题的数值解提供了一个基础．