Roland Gachechiladze and Otar Maisaia

Some Qualitative Problems of the Linear Elasticity Theory

The first and the second boundary value problems of statics are considered. The dependence of the solutions and of the corresponding eigenfrequencies of these problems on the elastic constants and density is investigated. The same dependence is studied for the total deformation energy and for Green's operators. The following theorem is proved: among anisotropic elastic convex bodies of a given volume there exists one for which the first eigenfrequency of the first boundary value problem is minimal.

Mathematics Subject Classification: 73C02

Key words and phrases: Elasticity, $n$-dimensional, boundary value problem, Green's operator, fundamental frequency, isoperimetric problem.