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Escobar type theorems for elliptic fully nonlinear degenerate equations
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 141, Number 5, October 2019
- pp. 1179-1216
- 10.1353/ajm.2019.0030
- Article
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Abstract
abstract:
In this paper we prove non-existence and classification results for elliptic fully nonlinear elliptic degenerate conformal equations on certain subdomains of the sphere with prescribed constant mean curvature along its boundary. We also consider non-degenerate equations. Such subdomains are geodesic balls in ${\Bbb S}^m$, punctured balls and annular domains.
Our results extend those of Escobar when $m\geq 3$, and Hang-Wang and Jim\'{e}nez when $m=2$.
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