We consider the evolution of a two–dimensional liquid droplet on a solid substrate in the,presence of a contact point. At the liquid-solid interface we assume Navier slip. At the triple point we assume a constant contact angle, given by Young’s law. The main result is well–posedness and regularity of the solution of the corresponding linearized problem in a class of weighted Sobolev spaces. This is a joint work with M. Bravin (U. Santander), M. Gnann (TU Delft), N. Masmoudi (NYU AD), F. Rodenburg (TU Delft), J. Sauer (U. Jena)