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An integral functional $I(w) = \int_{B} \left|\adj \nabla w\frac{w}{|w|^{3}}\right|^{q}$ defined on suitable maps $w$ is studied. Theinequality $I(w) \geq I(\mathbf{id})$, where $\mathbf{id}$ is the identity map,is established on a subclass of the admissible maps, and as such confirms inthese cases a criterion for the local minimality of the radial cavitating mapin 3 dimensional nonlinear elasticity. The criterion was first identified by J.Sivaloganathan and S. Spector in, "Necessary conditions for a minimum at aradial cavitating singularity in nonlinear elasticity. Ann. I. H. Poincare 25(2008) no.1, 201-213".

A remark on a stability criterion for the radial cavitating map in nonlinear elasticity