Global Morrey regularity results for asymptotically convex variational problems
Mikil Foss, Antonia Passarelli di Napoli, Anna Verde · Forum Mathematicum · 2008
We prove some global, up to the boundary of a domain Ω ⊂ ℝ n , continuity and Morrey regularity results for almost minimizers of functionals of the form . 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.