Interior curvature bounds for a class of curvature equations (Q701887)

In the present study the authors derive interior curvature bounds for admissible solutions of a class of curvature equations subject to affine Dirichlet data, generalizing the well-known interior second derivative bound for equations of Monge-Ampère type. In addition, in the case where convexity of the solution is the natural ellipticity assumption, the authors prove an interior curvature bound for convex solutions subject to \(C^{1,1}\) data. Moreover, they use the curvature bound to extend and to improve various existence results for the Dirichlet and Plateau problems.