Abstract
We consider a Yamabe-type problem on locally conformally flat compact manifolds with boundary. The main technique we used is to derive boundary C 2 estimates directly from boundary C 0 estimates. We will control the third derivatives on the boundary instead of constructing a barrier function. This result is a generalization of the work by Escobar.
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Chen, Sy.S. Boundary value problems for some fully nonlinear elliptic equations. Calc. Var. 30, 1–15 (2007). https://doi.org/10.1007/s00526-006-0072-7
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DOI: https://doi.org/10.1007/s00526-006-0072-7