The Dirichlet problem for Hessian type elliptic       equations on Riemannian manifolds

Bo  Guan; Heming  Jiao

doi:10.3934/dcds.2016.36.701

Article Contents

2016, Volume 36, Issue 2: 701-714. Doi: 10.3934/dcds.2016.36.701

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The Dirichlet problem for Hessian type elliptic equations on Riemannian manifolds

Bo Guan^1, and
Heming Jiao^2,

1.
Department of Mathematics, The Ohio State University, Columbus, OH 43210
2.
Department of Mathematics, Harbin Institute of Technology, Harbin, 150001

Received: June 30, 2014

Revised: December 31, 2014

Published: May 2017

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Abstract

We apply some new ideas to derive $C^2$ estimates for solutions of a general class of fully nonlinear elliptic equations on Riemannian manifolds under a ``minimal'' set of assumptions which are standard in the literature. Based on these estimates we solve the Dirichlet problem using the continuity method and degree theory.

Keywords:

Fully nonlinear elliptic equations on Riemannian manifolds,
a priori estimates,
Dirichlet problem,
subsolutions,
concavity.

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

Citation:

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