## Remarks on the regularity of the minimizers of certain degenerate functionals.(English)Zbl 0607.49003

The authors study the partial or global regularity of the minimizers for integrals functionals of the type $$\int_{\Omega}f(x,u,Du)dx$$ where $$\Omega$$ is a bounded open set in $${\mathbb{R}}^ n$$, $$u: \Omega\to {\mathbb{R}}^ N$$ and f is subjected to a growth condition in the last variable, which is polynomial like $$| p|^ m$$, $$m\geq 2$$. The treatment is very careful and articulate and includes also many hard cases as, for example, that of degenerate integrands. The theorems they obtain extend and improve various well-known results on the subject (see the references).