Geodesic
Schouten tensor equations in conformal geometry with prescribed boundary metric
Electronic journal of differential equations, Tome 2005 (2005)
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 
@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/}
}
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TI  - Schouten tensor equations in conformal geometry with prescribed boundary metric
JO  - Electronic journal of differential equations
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VL  - 2005
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%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
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/