Boundary value problems for some fully nonlinear elliptic equations
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- Chen, S.S. Calc. Var. (2007) 30: 1. doi:10.1007/s00526-006-0072-7
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We consider a Yamabe-type problem on locally conformally flat compact manifolds with boundary. The main technique we used is to derive boundary C2 estimates directly from boundary C0 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.