The Dirichlet Problem for Curvature Equations in Riemannian Manifolds

2012/04/26 by Jorge H. S. de Lira, de Lira, Jorge H. S., Flávio F. Cruz +1
Mathematics · #53A10 (Primary) #53C42 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A10 #msc:53C42

paper · pdf · doi:10.48550/arxiv.1204.5993

32 pages, no figures. Final version. Paper accepted to publication in Indiana University Mathematics Journal

arxiv created 2013/05/03 · arxiv updated 2013/05/07

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.

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