  For an n-dimensional bounded domain we derive some inequalities bounding the
norm of a square tensor field. Concerning the Div-Dev-inequality the bound is
given by the trace-free part and the divergence and the tensor. In the case of
the DevSym-Curl-inequality the bound is given by the trace-free and symmetric
part and the curl of the tensor. For n=3 the bound is given by the trace-free
symmetric part of the tensor and the trace-free part of the curl of the tensor.
Some prototype applications are presented in which the new inequalities may be
used to derive the coercivity of the models.
