On the existence and uniqueness of solution and some variational principles in linear theories of elasticity with couple-stresses. I: Cosserat continuum

summary:A weak (generalized) solution to the boundary-value problems in Cosserat continuum is defined. Its existence, uniqueness and continuous dependence upon the given data is proved for the statical loading of bounded, inhomogeneous and anisotropic bodies. Principles of minimum potential energy, of minimum complementary energy and some generalized variational principles are established