The Dirichlet problem for Hessian type elliptic equations on Riemannian manifolds

Bo Guan; Heming Jiao

doi:10.3934/dcds.2016.36.701

The Dirichlet problem for Hessian type elliptic equations on Riemannian manifolds

Bo Guan
, Heming Jiao

School of Mathematics

Ohio State University

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

We apply some new ideas to derive C² 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.

Original language	English
Pages (from-to)	701-714
Number of pages	14
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	36
Issue number	2
DOIs	https://doi.org/10.3934/dcds.2016.36.701
State	Published - 1 Feb 2016

Keywords

A priori estimates
Concavity
Dirichlet problem
Fully nonlinear elliptic equations on Riemannian manifolds
Subsolutions

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title = "The Dirichlet problem for Hessian type elliptic equations on Riemannian manifolds",

abstract = "We apply some new ideas to derive C2 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.",

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KW - A priori estimates

KW - Concavity

KW - Dirichlet problem

KW - Fully nonlinear elliptic equations on Riemannian manifolds

KW - Subsolutions

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The Dirichlet problem for Hessian type elliptic equations on Riemannian manifolds

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Keywords

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