*Published Paper*

**Inserted:** 1 feb 2002

**Last Updated:** 6 jul 2002

**Journal:** C. R. Acad. Sci. Paris Sér. I Math.

**Volume:** 328

**Number:** 4

**Pages:** 363-368

**Year:** 1999

**Abstract:**

Consider the following functional:
$$ \int

Du^{{p}(x)}\ dx $$
where: $u:\Omega \to R^N$. We prove that if $u$ is a minimizer then $Du$ is locally Hölder
continuous provided $p(x)>1$ is locally Hölder. This result is, of course, sharp.