Uniform integrability in periodic homogenization of fully nonlinear elliptic equations

Abstract This paper is devoted to the study of uniform $$W^{1,\frac{np}{n-p}}$$ W 1 , np n - p - and $$W^{2,p}$$ 2 -estimates for periodic homogenization problems fully nonlinear elliptic equations. We establish sharp, global, large-scale estimates under Dirichlet boundary conditions. The main novelty this can be found in characterization size “effective” Hessian gradient viscosity solutions problems. Moreover, work a large class non-convex It should stressed that our global are new even standard without homogenization.