Morrey regularity results for asymptotically convex variational problems with (p,q)(p,q) growth

We prove some global Morrey regularity results for almost minimizers of functionals of the formu↦∫Ωf(x,∇u)dx. This regularity is valid up to the boundary, provided the boundary data is sufficiently regular. The main assumption on f is that for each x  , the function f(x,⋅)f(x,⋅) behaves asymptotically like a convex function with (p,q)(p,q) growth. Some discontinuous behavior in the first argument is allowed. As a main application, we establish analogous regularity results for a broad class of systems of nonhomogeneous partial differential equations.