  We establish a comparison principle providing accurate upper bounds for the
modulus of vector valued minimizers of an energy functional, associated when
the potential is smooth, to elliptic gradient systems. Our assumptions are very
mild: we assume that the potential is lower semicontinuous, and satisfies a
monotonicity condition in a neighborhood of its minimum. As a consequence, we
give a sufficient condition for the existence of dead core regions, where the
minimizer is equal to one of the minima of the potential.
