Quantified Legendreness and the regularity of minima
A new quantification of nonuniform ellipticity in variational problems is proposed by means of convex duality. Higher differentiability and \(2D\)-smoothness results for vector-valued minimizers of possibly degenerate functionals are provided, and several significant special cases are discussed. Earlier results from [\textit{P. Marcellini}, Arch. Ration. Mech. Anal. 105, No. 3, 267--284 (1989; Zbl 0667.49032)] are rediscovered and improved.
scientific article; zbMATH DE number 7899611
scientific article