Sobre la solubilidad debil de problemas con valores en la frontera para sistemas elipticos

This paper concerns with existence and uniqueness of a weak solution for elliptic systems of partial di erential equations with mixed boundary conditions. The proof is based on establishing the coerciveness of bilinear forms, related with the system of equations, which depend on rst-order derivatives of vector functions in Rn. The condition of coerciveness relates to Korns type inequalities. The result is illustrated by an example of boundary value problems for a class of elliptic equations including the equations of linear elasticity.