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In this paper we prove a regularity result for local minimizers of functionals of the Calculus of Variations of the type $${\int }_{\Omega }f(x,Du)\mathrm{d}x$$ where Ω is a bounded open set in ${ℝ}^n$, u ∈ $W_{\mathrm{loc}}^{1,p}$(Ω; ${ℝ}^N$), p > 1, n ≥...