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 system with strong diffusional and elastic interactions between inclusions. The usual mean-field approximation breaks down and several independent length scales have to be taken into account. In a system of parallel oriented particles we find scaling laws for the coarsening of the different length scales involved. In particular, the lateral size of the particles obeys a nontrivial growth law, R ϳ t 5͞12 .PACS numbers: 81.10. Aj, 62.20.Mk, 81.40.Np The growth of crystals from the melt or from a solution is a typical example of first-order phase transition. Ostwald ripening is the late-stage process by which a new phase coarsens in order to lower the interfacial free energy. During this process the characteristic length scale of the precipitates increases in time, the supersaturation decreases, and the system moves towards phase equilibrium.The classical coarsening theory was given by Lifshitz, Slyozov, and Wagner (LSW) [1] in the framework of a mean-field approach which is valid in the limit of small volume fractions of the new phase. In this approach all precipitated particles are assumed to be spherical and remote from each other. If the diffusional transport of mass or heat is the limiting kinetics of the process, the average size of the particles grows with a power law in time with an exponent of 1͞3. The particle distribution function shows a characteristic scaling behavior.Novel aspects of kinetics of phase transitions appear if the initial metastable phase is a crystal. Generally, it is known that long-range elastic fields, which are inevitable in this situation, destroy the universal features of LSW growth, allowing other kinetics (see, for example, [2] and references therein). An oblate shape of the inclusions is often observed in experiments [3][4][5] and in computer simulations [2,6].Because of a difference in the densities of the two cooperating phases, part of the crystal surrounding a particle of the new phase becomes deformed if the slow diffusion of the point defects is neglected. This modifies the system's behavior in comparison to an unstressed situation. If one assumes incoherence at the interface, as is definitely the case for the melting process or for gas inclusions, the precipitates have an oblate shape which is more favorable compared to a spherical shape because of its lower elastic energy. This effect leads to a substantial modification of the laws of nucleation and growth [7,8].The main purpose of this Letter is to describe the last coarsening stage of this process which should also be very different from the one of classical LSW theory. The system inevitably arrives at a stage where the characteristic size of the particles is comparable to the distance between them. Indeed, if one assumes that these particles are very oblate lentils of radius R, height h ø R, and distance L between them, the volume fraction D 0 ϳ hR 2 ͞L 3 should remain ...