Published online by Cambridge University Press: 20 November 2018
By means of the Pucci operator, we construct a function ${{u}_{0}}$, which plays an essential role in our considerations, and give the existence and regularity theorems for the bounded viscosity solutions of the generalized Dirichlet problems of second order fully nonlinear elliptic equations on the general bounded domains, which may be irregular. The approximation method, the accretive operator technique and the Caffarelli's perturbation theory are used.
Permanent address: Department of Mathematics, Beijing Normal University, Beijing, 100875, People's Republic of China e-mail: [email protected]