Strong Static Stability of Liquid Layers

For a class of disjoining pressure potentials we show that liquid layers in equilibrium with positive second variation for nonvanishing variations (called stable by definition) are in fact strong minimizers of the associated energy functional. In a previous paper, explicit stable layers are obtained for some cases of solid configurations with simple geometries, in particular for a single cylindrical or spherical cavity. From this note it follows that all these “stable” equilibria are strong energy minimizers. No smallness for the thickness of the layer is assumed.