  We show that the following generalized version of Korn's second inequality
with nonconstant measurable matrix valued coefficients P
  ||DuP+(DuP)^T||_q+||u||_q >= c ||Du||_q for u in W_0^{1,q}({\Omega};R^3),
1<q<{\infty} is in general false, even if P is in SO(3), while the
Legendre-Hadamard condition and ellipticity on C^n for the quadratic form |Du
P+(DuP)^T|^2 is satisfied. Thus Garding's inequality may be violated for
formally positive quadratic forms.
