We investigate the regularity propertiesof local minimizers of non autonomous convex integral functionals of the type
with -growth into the gradient variable and discontinuous dependence on the variable. We prove a higher differentiability result for local minimizers of the functional assuming that the function that measures the oscillation of the integrand with respect to the variable belongs to a suitable Sobolev space.
Cite this article
Antonia Passarelli di Napoli, Regularity results for non-autonomous variational integrals with discontinuous coefficients. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 26 (2015), no. 4, pp. 475–496DOI 10.4171/RLM/717