Boundary estimates for a fully nonlinear Yamabe problem on Riemannian manifolds
Abstract
In this paper, we consider the Dirichlet boundary value problem for fully nonlinear Yamabe equations on Riemannian manifolds with boundary. Assuming the existence of a subsolution, we derive \emph{a priori} boundary second derivative estimates and consequently obtain the existence of a smooth solution. Moreover, with respect to a family of equations interpolating the fully nonlinear Yamabe equation and the classical semi-linear Yamabe equation, our estimates remain uniform. Finally, an example of a $C^1$ solution which is smooth in the interior but not smooth at the boundary is also given.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Advanced Mathematical Modeling in Engineering
Nonlinear Differential Equations Analysis
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems
- Volume
- 56
- Issue
- 0
- Pages
- 77–102
- Publication date
- 1 January 2026