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 ) = ∫ Ω F ( Dv ( x ))d x , 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.