The Dirichlet Problem for Curvature Equations in Riemannian Manifolds

摘要

We prove the existence of classical solutions to the Dirichlet problem for a class of fully nonlinear elliptic equations of curvature type on Riemannian manifolds. We also derive new second derivative boundary estimates which allow us to extend some of the existence theorems of Caffarelli, Nirenberg, and Spruck [4], and Ivochkina, Trudinger, and Lin [18], [19], [25] to more general curvature functions under mild conditions on the geometry of the domain.