ON THE EXISTENCE OF SMOOTH SOLUTIONS FOR FULLY NONLINEAR ELLIPTIC EQUATIONS WITH MEASURABLE 'COEFFICIENTS' WITHOUT CONVEXITY ASSUMPTIONS*

摘要

We show that for any uniformly elliptic fully nonlinear second-order equation with bounded measurable "coefficients" and bounded "free" term one can find an approximating equation which has a unique continuous and having the second derivatives locally bounded solution in a given smooth domain with smooth boundary data. The approximating equation is constructed in such a way that it modifies the original one only for large values of the unknown function and its derivatives.