Global higher integrability for minimisers of convex functionals with (p,q)-growth

Abstract

We prove global W 1,q (Ω, R m )-regularity for minimisers of convex functionals of the form F (u) = ´Ω F (x, Du) dx. W 1,q (Ω, R m ) regularity is also proven for minimisers of the associated relaxed functional. Our main assumptions on F (x, z) are a uniform α-Hölder continuity assumption in x and controlled (p, q)-growth conditions in z with q < (n+α)p n .Acknowledgements. L.K. was supported by the Engineering and Physical Sciences Research Council