Second derivative estimates for uniformly elliptic operators on Riemannian manifolds
The author obtains a uniform \(W^{2,\varepsilon}\)-estimate for solutions of the fully nonlinear uniformly elliptic equation NEWLINE\[NEWLINE F(D^2u,x)=f(x)\quad \text{in}\;B_R(z_0)\subset M, NEWLINE\]NEWLINE where \(M\) is a Riemannian manifold with lower bound for the sectional curvature. The approach relies on the Aleksandrov-Bakelman-Pucci method.
scientific article; zbMATH DE number 6366907