Asymptotically Quasiconvex Functionals with General Growth Conditions

We establish partial regularity results for minimizers of autonomous vectorial integrals in the Calculus of Variations, under ψ -growth conditions and assuming φ -quasiconvexity only in an asymptotic sense, both in subquadratic and superquadratic regimes. More precisely, we prove that minimizers are of class C 1 , α at points x 0 where D u is sufficiently large in a neighborhood of x 0 and where the excess is sufficiently small, and we obtain Lipschitz regularity on a dense open subset of the domain. These results apply to pairs of Young functions ( φ , ψ ) satisfying the structural assumptions ( H .0 ) – ( H .4 ) , which are strictly stronger than the classical Δ 2 condition.