Derivation of the LSW-theory for Ostwald ripening by homogenization methods

The coarsening of a solid phase in an undercooled liquid is described by a Stefan problem with surface tension. The solid phase is characterized by a large number of balls with small volume fraction and small capacity. We solve the quasi-static equation as well as the parabolic problem and construct approximate solutions by means of comparison principles. The framework of Young measures is used to pass to the limit of infinitely many particles. We obtain that the capacity is the crucial quantity to get the conservation law for the particle size distribution which is studied in the classical theory for Ostwald ripening by LIFSHITZ, SLYOZOV & WAGNER (LSW).