The obstacle problem for conformal metrics on compact Riemannian manifolds

机译：紧黎曼流形上保形度量的障碍问题

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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) arising from conformal deformation. With the a priori estimates the existence of a C^1,1 solution to the obstacle problem with Dirichlet boundary value is obtained by approximation.

机译：我们证明了针对共形形变引起的黎曼流形（M ^{n ，g）上曲率方程的障碍问题解的先验估计，可以得到其二阶导数。通过先验估计，通过逼近获得了Dirichlet边值问题的C ^{1,1 解的存在。}}

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期刊名称 Springer Open Choice
作者
Sijia Bao; Yuming Xing;
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作者单位

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年(卷),期 -1(2018),1
年度 -1
页码 238
总页数 12
原文格式 PDF
正文语种
中图分类外科学;
关键词
Obstacle problem A priori estimates Hessian equations Viscosity solutions Riemannian manifolds;

机译：障碍问题;先验估计;Hessian方程;粘度解;黎曼流形;

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专利

1. The obstacle problem for conformal metrics on compact Riemannian manifolds [J] . Sijia Bao, Yuming Xing Journal of inequalities and applications . 2018,第1期

机译：紧黎曼流形上保形度量的障碍问题
2. Compactness results in conformal deformations of Riemannian metrics on manifolds with boundaries [J] . Felli V., Ahmedou MO. Mathematische Zeitschrift . 2003,第1期

机译：紧致性导致带有边界的流形上的黎曼度量的共形变形
3. Compactness for conformal metrics with constant Q curvature on locally conformally flat manifolds [J] . Qing J, Raske D Calculus of variations and partial differential equations . 2006,第3期

机译：局部保形平坦歧管上具有恒定Q曲率的保形度量的紧度
4. INFINITESIMAL CONFORMAL TRANSFORMATIONS OF RIEMANNIAN MANIFOLDS WHICH PRESERVE THE GENERALIZED EINSTEIN TENSOR [C] . CHEREVKO Yevhen, BEREZOVSKII Vladimir, NENKA Ruslana, Conference on Applied Mathematics . 2020

机译：维持广义爱因斯坦张量的黎曼歧管的无限形象转化
5. The Role of Riemannian Manifolds in Computer Vision: From Coding to Deep Metric Learning [D] . Faraki, Masoud. 2018

机译：黎曼流形在计算机视觉中的作用：从编码到深度度量学习
6. ON THE GROUP OF CONFORMAL TRANSFORMATIONS OF A COMPACT RIEMANNIAN MANIFOLD [O] . Chuan-Chih Hsiung 1965

机译：关于紧黎曼流形的保角变换群
7. Compactness results in conformal deformations of Riemannian metrics on manifolds with boundaries [O] . V. Felli, M. Ould Ahmedou 2003

机译：紧凑率导致横向于歧管的黎曼指标的形象变形

The obstacle problem for conformal metrics on compact Riemannian manifolds

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