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On the Dirichlet problem for fully nonlinear elliptic equations on annuli of metric cones

Research supported in part by NSF in China, No. 11571288, No. 11671330, No. 11571332, No. 11625106 and No. 11131007.

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  • In this paper, we study a class of fully nonlinear elliptic equations on annuli of metric cones constructed from closed Sasakian manifolds and derive the a priori estimates assuming the existence of subsolutions. Moreover, such a priori estimates can be applied to certain degenerate equations. A condition for the solvability of Dirichlet problem for non-degenerate fully nonlinear elliptic equations is discovered. Furthermore, we also discuss degenerate equations.

    Mathematics Subject Classification: 35J15, 35J70, 58J05, 35B45.


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