Regularity issues for orthotropic functionals

We present a class of integral convex functionals from the Calculus of Variations,
exhibiting a severe degeneracy, in despite of their very simple structure. We discuss
gradient regularity for local minimizes, by giving some boundedness and continuity
results. The case of nonstandard growth conditions is included, as well. In the final
part, we will present some perspectives and open problems.
The results presented are part of a research project headed in collaboration with
Pierre Bousquet (Toulouse).