On the general notion of fully nonlinear second-order elliptic equations

The general notion of fully nonlinear second-order elliptic equation is given. Its relation to so-called Bellman equations is investigated. A general existence theorem for the equations like Pₘ(u_xⁱxʲ) = ∑ k = 0m - 1 cₖ(x)Pₖ(u_xⁱxʲ) is obtained as an example of an application of the general notion of fully nonlinear elliptic equations.