A 2-D free boundary problem with onset of a phase and singular elliptic boundary value problems. (Q1565960)

The author studies a two-dimensional elliptic free boundary problem representing the quasi-steady version of diffusion of solvents through glassy polymers. The diffusion domain is initially degenerate. The normal velocity of the interface is, as usual, supposed to be proportional to a power of the solvent concentration, but here a curvature dependent term is added. The problem is reformulated in a fixed domain by means of a singular transformation, emphasizing the leading singularity. A Fourier transform technique is applied to prove existence and uniqueness of a classical solution.