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

Chunhui Qiu; Rirong Yuan

doi:10.3934/dcds.2017247

Article Contents

2017, Volume 37, Issue 11: 5707-5730. Doi: 10.3934/dcds.2017247

This issue Previous Article 2-manifolds and inverse limits of set-valued functions on intervals Next Article A Liouville theorem for indefinite fractional diffusion equations and its application to existence of solutions

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

Chunhui Qiu and
Rirong Yuan

School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

Received: April 30, 2017

Published: October 2017

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

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Abstract

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.

Keywords:

Sasakian manifold,
metric cone,
degenerate fully nonlinear elliptic equation,
a priori estimates,
Dirichlet problem,
subsolution,
cone condition,
concavity.

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

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