(untitled) (Journal of Partial Differential Equations, 1991)
We consider the problem of existence for viscosity solutions of seoond order fully nonlinear elliptic partial differential equations F(D&sup2u, Du, u, z) = 0. We prove existence results for viscosity solutions in W^1,&#8734 under assumptions that function F satisfies the natural structure conditions. We do not assume F is convex.