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.
Cite this article
Flavia Giannetti, Antonia Passarelli di Napoli, Regularity results for minimizers of integral functionals with nonstandard growth in Carnot–Carathéodory spaces. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 21 (2010), no. 2, pp. 175–192DOI 10.4171/RLM/566