  We consider second order elliptic systems of partial differential equations
subject to Dirichlet and Neumann boundary conditions. We prove analyticity of
the elementary symmetric functions of the eigenvalues, and compute
Hadamard-type formulas for such functions. Then we provide a characterization
of criticality of the domain under volume constraint, and prove that if the
system is rotation invariant, then balls are critical domains for all those
functions.
