Higher integrability for constrained minimizers of integral functionals with (p, q)-growth in low dimension

We prove higher summability for the gradient of minimizers of strongly convex integral functionals of the Calculus of Variations ˆ Ω f(x, Du(x)) dx, u : Ω ⊂ R n → S N−1 , with growth conditions of (p, q)-type: |ξ| p ≤ f(x, ξ) ≤ C(|ξ| q + 1), p < q, in low dimension. Our procedure is set in the framework of Fractional Sobolev Spaces and renders the desired regularity as the result of an approximation technique relying on estimates obtained through a careful use of difference quotients.