THE DIRICHLET PROBLEM FOR DEGENERATE FULLY NONLINEAR ELLIPTIC EQUATIONS ON RIEMANNIAN MANIFOLDS

被引:0
作者
Yuan, Rirong [1 ]
机构
[1] South China Univ Technol, Sch Math, Guangzhou 510641, Peoples R China
基金
中国国家自然科学基金;
关键词
HESSIAN EQUATIONS; REGULARITY; DUALITY;
D O I
暂无
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We derive the existence of C1,1-solutions to the Dirichlet problem for degenerate fully nonlinear elliptic equations on Riemannian manifolds under appropriate assumptions.
引用
收藏
页码:3931 / 3946
页数:16
相关论文
共 35 条
[1]   Monge-Ampere Equations on Complex Manifolds with Boundary [J].
Boucksom, Sebastien .
COMPLEX MONGE-AMPERE EQUATIONS AND GEODESICS IN THE SPACE OF KAHLER METRICS, 2012, 2038 :257-282
[2]   THE DIRICHLET PROBLEM FOR NONLINEAR 2ND-ORDER ELLIPTIC-EQUATIONS .3. FUNCTIONS OF THE EIGENVALUES OF THE HESSIAN [J].
CAFFARELLI, L ;
NIRENBERG, L ;
SPRUCK, J .
ACTA MATHEMATICA, 1985, 155 (3-4) :261-301
[3]  
Caffarelli LuisA., 1986, Rev. Mat. Iberoamericana, V2, P19, DOI 10.4171/RMI/23
[4]  
Chen XX, 2000, J DIFFER GEOM, V56, P189, DOI 10.4310/jdg/1090347643
[5]   LIOUVILLE AND CALABI-YAU TYPE THEOREMS FOR COMPLEX HESSIAN EQUATIONS [J].
Dinew, Slawomir ;
Kolodziej, Slawomir .
AMERICAN JOURNAL OF MATHEMATICS, 2017, 139 (02) :403-415
[6]   Hessian equations with elementary symmetric functions [J].
Dong, HJ .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2006, 31 (07) :1005-1025
[8]   BOUNDARY-VALUE-PROBLEMS ON S(N) FOR SURFACES OF CONSTANT GAUSS CURVATURE [J].
GUAN, B ;
SPRUCK, J .
ANNALS OF MATHEMATICS, 1993, 138 (03) :601-624
[9]   The Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifolds [J].
Guan, Bo .
ADVANCES IN MATHEMATICS, 2023, 415
[10]   ON ESTIMATES FOR FULLY NONLINEAR PARABOLIC EQUATIONS ON RIEMANNIAN MANIFOLDS [J].
Guan, Bo ;
Shi, Shujun ;
Sui, Zhenan .
ANALYSIS & PDE, 2015, 8 (05) :1145-1164