abstract: The formation and assembly patterns of quantum dots play a central role on the optoelectronic properties of semiconductors. We will address quasistatic equilibria and regularity of islands (quantum dots), and using De Giorgi’s minimizing movements we will obtain short time existence for a surface diffusion evolution equation with curvature regularization in the context of epitaxially strained fi A variational model for the nucleation of misfi dislocations will be analyzed. This is joint work with Nicola Fusco, Giovanni Leoni, and Massimiliano Morini