Geodesic
Schouten tensor equations in conformal geometry with prescribed boundary metric
Electronic journal of differential equations, Tome 2005 (2005)
Zbl   arXiv   EuDML
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.
Classification : 53A30, 35J25, 58J32
Keywords: Schouten tensor, fully nonlinear equation, conformal geometry, Dirichlet boundary value problem 
Schnürer,  Oliver C. Schouten tensor equations in conformal geometry with prescribed boundary metric. Electronic journal of differential equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a66/
@article{EJDE_2005__2005__a66,
     author = {Schn\"urer,  Oliver C.},
     title = {Schouten tensor equations in conformal geometry with prescribed boundary metric},
     journal = {Electronic journal of differential equations},
     year = {2005},
     volume = {2005},
     zbl = {1074.53032},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a66/}
}
TY  - JOUR
AU  - Schnürer,  Oliver C.
TI  - Schouten tensor equations in conformal geometry with prescribed boundary metric
JO  - Electronic journal of differential equations
PY  - 2005
VL  - 2005
UR  - http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a66/
LA  - en
ID  - EJDE_2005__2005__a66
ER  - 
%0 Journal Article
%A Schnürer,  Oliver C.
%T Schouten tensor equations in conformal geometry with prescribed boundary metric
%J Electronic journal of differential equations
%D 2005
%V 2005
%U http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a66/
%G en
%F EJDE_2005__2005__a66