On the growth of nonconvex functionals at strict local minimizers

Abstract: We give new characterizations of growth conditions at strict local minimizers. The main characterizations are a variant of the so-called tilt stability property and an analog of the classical Polyak--\L{}ojasiewicz condition, where the gradient is replaced by linear perturbations. As a consequence, we derive a tilting principle that relates the stability of minimizers under linear perturbations to their stability under nonlinear ones.