On extremals of a variational problem arising in crystallography

In this paper we study the structure of minirnizers of variational problems which were introduced by Hannon, Marcus and Mizel (ESAIM Control Optim. Calc. Var., 2003) to describe step-terraces on surfaces of so-called "unorthodox" crystals. These variational problems are associated with two positive parameters. We will show that if one of these parameters is not smali and the second parameter is large, then the rainimizer is a constant function.