Two-dimensional islanding atop stressed solid helium and epitaxial films

We discuss the role of stress in destabilizing flat surfaces of thin solid films. The presence of this instability in stressed ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and several heteroepitaxial films is widely acknowledged and well documented. We pay special attention to the study of possible in-plane morphologies of the islands which appear as a result of the stress-driven destabilization of flat traction-free interfaces. We also discuss the critical thickness at which these morphologies change.