Partial regularity of strong local minimizers of quasiconvex integrals with (p, q)-growth

Abstract

We consider strictly quasiconvex integrals

in the multi-dimensional calculus of variations. For the C²-integrand f : ℝ^Nn → ℝ we impose (p, q)-growth conditions

with γ, Γ > 0 and 1 < p ≤ q < min {p + 1/n, p(2n − 1)/(2n − 2)}. Under these assumptions we prove partial C^{1, α}_loc-regularity for strong local minimizers of F and the associated relaxed functional .