The Dirichlet Problem for Curvature Equations in Riemannian Manifolds
Differential Geometry
2013-05-07 v3
Abstract
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 allows us to extend some of the existence theorems of Caffarelli, Nirenberg and Spruck [4] and Ivochkina, Trundinger and Lin [19] to more general curvature functions and less convex domains.
Keywords
Cite
@article{arxiv.1204.5993,
title = {The Dirichlet Problem for Curvature Equations in Riemannian Manifolds},
author = {Jorge H. S. de Lira and Flávio F. Cruz},
journal= {arXiv preprint arXiv:1204.5993},
year = {2013}
}
Comments
32 pages, no figures. Final version. Paper accepted to publication in Indiana University Mathematics Journal