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$ C^{1,1}$ regularity for an obstacle problem of Hessian equations on Riemannian manifolds


Author: Heming Jiao
Journal: Proc. Amer. Math. Soc. 144 (2016), 3441-3453
MSC (2010): Primary 35B45, 35B65, 58J32
DOI: https://doi.org/10.1090/proc/12988
Published electronically: February 2, 2016
MathSciNet review: 3503712
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Abstract: In this paper, we study an obstacle problem for a class of fully nonlinear equations on Riemannian manifolds. Using some new ideas, the $ C^{1,1}$ regularity for the greatest viscosity solution is established under essentially optimal structure conditions.


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Additional Information

Heming Jiao
Affiliation: Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China
Email: jiao@hit.edu.cn

DOI: https://doi.org/10.1090/proc/12988
Keywords: Obstacle problem, Riemannian manifolds, fully nonlinear equations, $C^{1, 1}$ regularity
Received by editor(s): April 3, 2015
Received by editor(s) in revised form: September 30, 2015
Published electronically: February 2, 2016
Additional Notes: This work was supported by the Fundamental Research Funds for the Central Universities and Program for Innovation Research of Science in Harbin Institute of Technology, No. 61509066.
Communicated by: Guofang Wei
Article copyright: © Copyright 2016 American Mathematical Society

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