Abstract: The completeness of the solutions of Boussinesq and Love has been proved by Noll and Gurtin if the four hypotheses about an elastic region are satisfied. In this paper, it is proved that the four hypotheses about the elastic region are unnecessary for the completeness of Boussinesq's solution and that only two hypotheses are sufficient for the completeness of Love's solution.

Key words: elasticity, general solution, completeness

摘要： 如果弹性区域满足4个条件，Noll和Gurtin证明了Boussinesq和Love解是完备的。在本文中，将证明对Boussinesq解的完备性而言，上述4个假设是不必要的，而对Love解的完备性，只需2个假设就足够了。

关键词: 弹性力学, 弹性通解, 完备性