Hölder regularity for a classical problem of the calculus of variations
Carlo Mariconda, Giulia Treu · Advances in Calculus of Variations · 2009
Abstract Let be bounded, open and convex. Let be convex, coercive of order p > 1 and such that the diameters of the projections of the faces of the epigraph of F are uniformly bounded. Then every minimizer of is Hölder continuous in of order whenever φ is Lipschitz on ∂Ω. A similar result for non convex Lagrangians that admit a minimizer follows.