Regularity results for minimizers of integral functionals with nonstandard growth in Carnot–Carathéodory spaces

Abstract

We prove regularity results for minimizers of integral functionals of the type

where $f$ satisfies a nonstandard growth condition and $Xu$ stands for the horizontal gradient of $u$. More precisely, we obtain regularity in the scale of Campanato spaces without assuming any restriction on the growth exponents and, under a suitable assumption on them, we get the local boundedness as well as an higher integrability result for the gradient.