Global higher integrability for minimisers of convex functionals with

I present a global W^1,q(Ω,Rm)-regularity result for minimisers of convex functionals of the form F(u) =∫Ω f(x, Du) dx  with (p,q)-growth. Further Idiscuss a global W^1,q-regularity result for a relaxed functional related to F(u).