The nucleation and growth of facets on stepped Si(111) have been observed in real time using the newly developed technique of low-energy electron microscopy (LEEM). The results show that the growth of an isolated facet spontaneously stops at a well-defined size. This is a surprise as classical theories of the growth of linear facets predict a continuous growth, which would only be limited by collisions with neighboring facets. We review predictions that elastic interactions between surface regions of different structure can stabilize finite size domains and facets. We show that a model in which elastic relaxations caused by the facet boundaries stabilize a finite facet width is entirely consistent with the experimental observations.