Key points are not available for this paper at this time.
Abstract We introduce a new quantification of nonuniform ellipticity in variational problems via convex duality, and prove higher differentiability and 2 d -smoothness results for vector valued minimizers of possibly degenerate functionals. Our framework covers convex, anisotropic polynomials as prototypical model examples—in particular, we improve in an essentially optimal fashion Marcellini’s original results (Marcellini in Arch Rat Mech Anal 105:267–284, 1989).
Filippis et al. (Mon,) studied this question.