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 ∫Ωf(x,Du(x))dx,u:Ω⊂Rn→SN−1,with growth conditions of (p,q)-type: |ξ|p≤f(x,ξ)≤C(|ξ|q+1),p