Local and asymptotic regularity results for quasiconvex and quasimonotone problems

Considering vectorial integrals in the multidimensional calculus of variations and quasilinear ellipticsystems of partial differential equations, we prove gradient regularity of minimizers and weaksolutions, respectively. In contrast to the classical theory, we impose our assumptions on the structurefunctions only locally (i.e. near a single point) or asymptotically (i.e. near infinity). In particular,we point out relations between the local and the asymptotic point of view, and we discuss notionsof quasiconvexity at infinity and quasimonotonicity at infinity, which arise in this context.