Inserted: 16 nov 2006
Last Updated: 13 apr 2010
Journal: Continuum Mech. Thermodyn.
Prompted by recent works on line tension effects upon the stability of liquid droplets laid on a rigid substrate, we prove existence and stability of equilibrium configurations when the substrate is either planar or spherical. For positive line tension our argument involves only set symmetrization, while for negative line tension a stability criterion is proposed which makes variational problems well-posed in the framework of sets with finite perimeter. Several applications illustrate the role of the criterion in providing a natural cutoff length that selects physically meaningful destabilizing modes.