Uniform Estimates in Periodic Homogenization of Fully Nonlinear Elliptic Equations

Abstract This article is concerned with uniform $$C^{1,\alpha }$$ C 1 , ? and $$C^{1,1}$$ estimates in periodic homogenization of fully nonlinear elliptic equations. The analysis based on the compactness method, which involves linearization operator at each approximation step. Due to nonlinearity equations, linearized operators involve Hessian correctors, appear previous involvement correctors deteriorates regularity operator, sometimes even changes its oscillating pattern. These issues are resolved new techniques, yield a precise decomposition regular part irregular process, along control an intermediate level. techniques context linear Our argument can be applied not only concave operators, but also certain class non-concave operators.