Global Morrey regularity results for asymptotically convex variational problems

We prove some global, up to the boundary of a domain Omega subset of R-n, continuity and Morrey regularity results for almost minimizers of functionals of the form u bar right arrow integral(Omega) g(x, u(x), del u(x)) dx. The main assumptions are that g is asymptotically convex and that it has superlinear polynomial growth with respect its third argument. The integrand is only required to be locally bounded with respect to its third argument. Some discontinuous behavior with respect to its other arguments is also allowed. We also provide an application of our results to a class of variational problems with obstacles.