A combined capillarity and elasticity problem for a thin plate

The equilibrium of an elastic thin plate in contact with a drop of fluid (both surrounded by another fluid), including capillarity (i.e., the thermodynamic properties of the fluid-fluid and solid-fluid surfaces), leads to a variational problem with discontinuities of some derivatives of the elastic displacement of the plate at the solid-fluid-fluid contact line. Owing to the elasticity of the solid, the classical capillary Young's equation is modified.