Volume 48, Issue 3
Second Order Estimates for Non-Concave Hessian Type Elliptic Equations on Riemannian Manifolds

J. Math. Study, 48 (2015), pp. 275-289.

Published online: 2015-09

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• Abstract

In this paper, we derive second order estimates for a class of non-concave Hessian type elliptic equations on Riemannian manifolds. By applying a new method for $C^2$ estimates, we can weaken some conditions, which works for some non-concave equations. Gradient estimates are also obtained.

• Keywords

Non-concave fully nonlinear elliptic equations, Riemannian manifolds, a priori estimates, Dirichlet problem, subsolutions.

35J15, 58J05, 35B45

jiao@hit.edu.cn (Heming Jiao)

• BibTex
• RIS
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@Article{JMS-48-275, author = {Jiao , Heming}, title = {Second Order Estimates for Non-Concave Hessian Type Elliptic Equations on Riemannian Manifolds}, journal = {Journal of Mathematical Study}, year = {2015}, volume = {48}, number = {3}, pages = {275--289}, abstract = {

In this paper, we derive second order estimates for a class of non-concave Hessian type elliptic equations on Riemannian manifolds. By applying a new method for $C^2$ estimates, we can weaken some conditions, which works for some non-concave equations. Gradient estimates are also obtained.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v48n3.15.06}, url = {http://global-sci.org/intro/article_detail/jms/9930.html} }
TY - JOUR T1 - Second Order Estimates for Non-Concave Hessian Type Elliptic Equations on Riemannian Manifolds AU - Jiao , Heming JO - Journal of Mathematical Study VL - 3 SP - 275 EP - 289 PY - 2015 DA - 2015/09 SN - 48 DO - http://doi.org/10.4208/jms.v48n3.15.06 UR - https://global-sci.org/intro/article_detail/jms/9930.html KW - Non-concave fully nonlinear elliptic equations, Riemannian manifolds, a priori estimates, Dirichlet problem, subsolutions. AB -

In this paper, we derive second order estimates for a class of non-concave Hessian type elliptic equations on Riemannian manifolds. By applying a new method for $C^2$ estimates, we can weaken some conditions, which works for some non-concave equations. Gradient estimates are also obtained.

Heming Jiao. (2019). Second Order Estimates for Non-Concave Hessian Type Elliptic Equations on Riemannian Manifolds. Journal of Mathematical Study. 48 (3). 275-289. doi:10.4208/jms.v48n3.15.06
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