Original Article

Calculus of Variations and Partial Differential Equations

, Volume 30, Issue 1, pp 1-15

First online:

Boundary value problems for some fully nonlinear elliptic equations

  • Szu-yu Sophie ChenAffiliated withDepartment of Mathematics, Princeton UniversityDepartment of Mathematics, University of California Email author 

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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 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.

Mathematics Subject Classification

35 53