Boundary estimates for a fully nonlinear Yamabe problem on Riemannian manifolds
Analysis of PDEs
2025-11-04 v1 Differential Geometry
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 solution which is smooth in the interior but not smooth at the boundary is also given.
Keywords
Cite
@article{arxiv.2511.01130,
title = {Boundary estimates for a fully nonlinear Yamabe problem on Riemannian manifolds},
author = {Weisong Dong and Yanyan Li and Luc Nguyen},
journal= {arXiv preprint arXiv:2511.01130},
year = {2025}
}