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

∫Ω f(Xu)dx

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.