The obstacle problem for conformal metrics on compact Riemannian manifolds

Sijia Bao; Yuming Xing

doi:10.1186/s13660-018-1827-3

The obstacle problem for conformal metrics on compact Riemannian manifolds

Sijia Bao^*
, Yuming Xing

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology

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

Abstract

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.

Original language	English
Article number	238
Journal	Journal of Inequalities and Applications
Volume	2018
DOIs	https://doi.org/10.1186/s13660-018-1827-3
State	Published - 2018

Keywords

A priori estimates
Hessian equations
Obstacle problem
Riemannian manifolds
Viscosity solutions

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10.1186/s13660-018-1827-3

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@article{2618b0d96de5438d9a82b8affacaa6d3,

title = "The obstacle problem for conformal metrics on compact Riemannian manifolds",

abstract = "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 C1 , 1 solution to the obstacle problem with Dirichlet boundary value is obtained by approximation.",

keywords = "A priori estimates, Hessian equations, Obstacle problem, Riemannian manifolds, Viscosity solutions",

author = "Sijia Bao and Yuming Xing",

note = "Publisher Copyright: {\textcopyright} 2018, The Author(s).",

year = "2018",

doi = "10.1186/s13660-018-1827-3",

language = "英语",

volume = "2018",

journal = "Journal of Inequalities and Applications",

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TY - JOUR

T1 - The obstacle problem for conformal metrics on compact Riemannian manifolds

AU - Bao, Sijia

AU - Xing, Yuming

PY - 2018

Y1 - 2018

N2 - 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 C1 , 1 solution to the obstacle problem with Dirichlet boundary value is obtained by approximation.

AB - 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 C1 , 1 solution to the obstacle problem with Dirichlet boundary value is obtained by approximation.

KW - A priori estimates

KW - Hessian equations

KW - Obstacle problem

KW - Riemannian manifolds

KW - Viscosity solutions

UR - https://www.scopus.com/pages/publications/85053238084

U2 - 10.1186/s13660-018-1827-3

DO - 10.1186/s13660-018-1827-3

M3 - 文章

AN - SCOPUS:85053238084

SN - 1025-5834

VL - 2018

JO - Journal of Inequalities and Applications

JF - Journal of Inequalities and Applications

M1 - 238

ER -

The obstacle problem for conformal metrics on compact Riemannian manifolds

Abstract

Keywords

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