Analytical validation of variational models for epitaxially strained thin films

The derivation of variational models describing the epitaxial growth of thin films in the framework of the theory of Stress-Driven Rearrangement Instabilities (SDRI) will be presented, and the state of the art of the mathematical results described. By working in the context of both continuum and molecular mechanics, not only free boundary problems, but also atomistic models will be considered, and the discrete-to-continuum passage rigorously investigated in the intent to also provide a microscopical justification of the theory. An overview of the mathematical results achieved through the years with various co-authors for the existence, regularity and evolution of the solutions will be presented.