Partial regularity of local minimizers of quasiconvex integrals with sub-quadratic growth

Abstract

We prove partial regularity for local minimizers of quasiconvex integrals of the form I(v) = ∫_ΩF(Dv(x))dx, where the integrand f(ξ) has sub-quadratic growth, i.e. |F(ξ)| ≤ L(1 + |ξ|^p), with 1 < p < 2. A function u ∈ W^1,p(Ω;R^N) is a W^1,q(Ω;R^N) local minimizer of I(v) if there exists a δ > 0 such that I(u) ≤ I(v) whenever v and ‖Dv − Du‖_q ≤ δ.