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.

Keywords:

Pucci operator, viscosity solution, existence, $C^{2, \psi}$ regularity, Dini condition, fully nonlinear equation, general domain, accretive operator, approximation lemma Pucci operator, viscosity solution, existence, $C^{2, \psi}$ regularity, Dini condition, fully nonlinear equation, general domain, accretive operator, approximation lemma

MSC Classifications:

35D05, 35D10, 35J60, 35J67 show english descriptions Existence of generalized solutions
Regularity of generalized solutions
Nonlinear elliptic equations
Boundary values of solutions to elliptic equations 35D05 - Existence of generalized solutions
35D10 - Regularity of generalized solutions
35J60 - Nonlinear elliptic equations
35J67 - Boundary values of solutions to elliptic equations

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