## Schouten tensor equations in conformal geometry with prescribed boundary metric

2005
Journal article
Published
##### Published in
Electronic Journal of Differential Equations (EJDE) ; 2005. - 81. - eISSN 1072-6691
##### 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.
510 Mathematics
##### Keywords
Schouten tensor; fully nonlinear equation; conformal geometry; Dirichlet boundary value problem
##### Cite This
ISO 690SCHNÜRER, Oliver C., 2005. Schouten tensor equations in conformal geometry with prescribed boundary metric. In: Electronic Journal of Differential Equations (EJDE), 81. eISSN 1072-6691
BibTex
@article{Schnurer2005Schou-41193,
year={2005},
title={Schouten tensor equations in conformal geometry with prescribed boundary metric},
url={https://eudml.org/doc/125235},
journal={Electronic Journal of Differential Equations (EJDE)},
author={Schnürer, Oliver C.},
note={Article Number: 81}
}

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2018-01-15
No