1. Understand the nature of unbalanced problems with variable growth
2. Identify regularity property of minimizers and distinguish degenerate models associated to anisotropic double phase problems
3. Interpret new critical and supercritical settings.
4. Recognize concentration phenomena for the spectrum of anisotropic operators.
5.  Solving new optimization problems (in control and nonlinear shell theory).
6. Understand unbalanced anisotropic problems on fractal sets.