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Keywords:

  • Liquid phase epitaxy with elasticity;
  • two scale model;
  • iterative procedure;
  • existence and regularity of solutions.

Abstract

Epitaxy is a technically relevant process since it gives the possibility to generate microstructures of different morphologies. These microstructures can be influenced by elastic effects in the epitaxial layer. We consider a two scale model including elasticity, introduced in [8]. The coupling of the microscopic and the macroscopic equations is described by an iterative procedure. We concentrate on the microscopic equations and study their solvability in appropriate function spaces. As the main results we prove the existence and uniqueness of solutions of the three single parts of the microscopic problem. The composition of the corresponding solution operators maps a suitable function space into itself. These results are a first step in the proof of existence of solutions via suitable fixed point arguments of the fully coupled two scale model.