A Haar-Rado type theorem for minimizers in Sobolev spaces
Let be a minimum for where f is convex, is convex for a.e. x. We prove that u shares the same modulus of continuity of ϕ whenever Ω is sufficiently regular, the right derivative of g satisfies a suitable monotonicity assumption and the following inequality holds This result generalizes the classical Haar-Rado theorem for Lipschitz functions.