On the existence and uniqueness of solution and some variational principles in linear theories of elasticity with couple-stresses. II. Mindlin's elasticity with microstructure and the first strain-gradient theory

summary:A weak solution to the boundary-value problems both in the Mindlin's theory of elasticity with microstructure and in the first strain-gradient theory is defined for the statical loading of bounded, inhomogeneous and anisotropic bodies. Its existence, uniqueness and continuous dependence upon the given data is proved and the principles of minimum potential energy and minimum complementary energy are establshed