Methods and Applications of Analysis
Volume 19 (2012)
On the existence of smooth solutions for fully nonlinear elliptic equations with measurable “coefficients” without convexity assumptions
Pages: 119 – 146
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.
fully nonlinear elliptic equations, Bellman’s equations, finite differences
2010 Mathematics Subject Classification