We discuss the coarsening process of melt inclusions inside a solid phase.
Elastic effects lead to an oblate shape of the particles, resulting in a sy
stem with strong diffusional and elastic interactions between inclusions. T
he usual mean-field approximation breaks down and several independent lengt
h scales have to be taken into account. In a system of parallel oriented pa
rticles we find scaling laws for the coarsening of the different length sca
les involved. In particular, the lateral size of the particles obeys a nont
rivial growth law, R similar to t(5/12).