The obstacle problem for conformal metrics on compact Riemannian manifolds

被引：0
作者：
Sijia Bao
Yuming Xing
机构：
[1] Harbin Institute of Technology,Department of Mathematics
来源：
Journal of Inequalities and Applications | / 2018卷
关键词：
Obstacle problem; A priori estimates; Hessian equations; Viscosity solutions; Riemannian manifolds;
D O I：
暂无
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学科分类号：
摘要：
We prove a priori estimates up to their second order derivatives for solutions to the obstacle problem of curvature equations on Riemannian manifolds (Mn,g)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(M^{n}, g)$\end{document} arising from conformal deformation. With the a priori estimates the existence of a C1,1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$C^{1,1} $\end{document} solution to the obstacle problem with Dirichlet boundary value is obtained by approximation.
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