Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 81, pp. 1-17.
Title: Schouten tensor equations in conformal geometry
with prescribed boundary metric
Author: Oliver C. Schnuerer (Freie Univ., Berlin, Germany)
Abstract:
We deform the metric conformally on a manifold with boundary.
This induces a deformation of the Schouten tensor. We fix the
metric at the boundary and realize a prescribed value for the
product of the eigenvalues of the Schouten tensor in the interior,
provided that there exists a subsolution.
This problem reduces to a Monge-Ampere equation with gradient
terms. The main issue is to obtain a priori estimates for the
second derivatives near the boundary.
Submitted March 15, 2004. Published July 15, 2005.
Math Subject Classifications: 53A30; 35J25; 58J32.
Key Words: Schouten tensor; fully nonlinear equation;
conformal geometry; Dirichlet boundary value problem.