New Challenges on the Regularity of Minimizers of Functionals

Our aim is to obtain regularity of minimizers of functionals under the nonstandard growth conditions. Starting point is the study made by the authors finalized to investigate the regularity of the minimizers of quadratic functionals, whose integrands have vanishing mean oscillation coefficients, using some majorizations for the functionals, rather than the well known Euler's equation associated with it.