Smooth approximations of solutions to nonconvex fully nonlinear elliptic equations
Luis A. Caffarelli, Luís Silvestre · Translations - American Mathematical Society/Translations · 2010
We show that fully nonlinear elliptic PDEs (which may not have classical solutions) can be approximated with integro-differential equations which have C 2,α solutions. For these approximated equations we prove a uniform C 1,α estimate. We also study the rate of convergence.