The Dirichlet Problem for Curvature Equations in Riemannian Manifolds

被引：1

作者：

de Lira, Jorge H. S. ^{[1
]}

Cruz, Flavio F. ^{[2
]}

机构：

[1] Univ Fed Ceara, Dept Matemat, BR-60455760 Fortaleza, Ceara, Brazil

[2] Univ Reg Cariri, Dept Matemat, BR-63041141 Juazeiro Do Norte, Ceara, Brazil

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2013年 / 62卷 / 03期

关键词：

Fully nonlinear elliptic PDEs; curvature equations; CONSTANT MEAN-CURVATURE; LOCALLY CONVEX HYPERSURFACES; NONLINEAR ELLIPTIC-EQUATIONS; PRESCRIBED GAUSS CURVATURE; BOUNDARY-VALUE-PROBLEMS; MONGE-AMPERE EQUATIONS; HESSIAN EQUATIONS; X R; GRAPHS; EXISTENCE;

D O I：

10.1512/iumj.2013.62.4996

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the existence of classical solutions to the Dirichlet problem for a class of fully nonlinear elliptic equations of curvature type on Riemannian manifolds. We also derive new second derivative boundary estimates which allow us to extend some of the existence theorems of Caffarelli, Nirenberg, and Spruck [4], and Ivochkina, Trudinger, and Lin [18], [19], [25] to more general curvature functions under mild conditions on the geometry of the domain.

引用

页码：815 / 854

页数：40

共 50 条

[41] MULTIPLE SOLUTIONS FOR NONLINEAR ELLIPTIC EQUATIONS ON RIEMANNIAN MANIFOLDS [J].

Chen, Wenjing ;

Yang, Jianfu .

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2009,

[42] FRACTIONAL p-LAPLACIAN EQUATIONS ON RIEMANNIAN MANIFOLDS [J].

Guo, Lifeng ;

Zhang, Binlin ;

Zhang, Yadong .

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2018,

[43] The Dirichlet problem for a complex Hessian equation on compact Hermitian manifolds with boundary [J].

Gu, Dongwei ;

Ngoc Cuong Nguyen .

ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2018, 18 (04) :1189-1248

[44] Positive solutions of the discrete Dirichlet problem involving the mean curvature operator [J].

Ling, Jiaoxiu ;

Zhou, Zhan .

OPEN MATHEMATICS, 2019, 17 :1055-1064

[45] The obstacle problem for conformal metrics on compact Riemannian manifolds [J].

Sijia Bao ;

Yuming Xing .

Journal of Inequalities and Applications, 2018

[46] The obstacle problem for conformal metrics on compact Riemannian manifolds [J].

Bao, Sijia ;

Xing, Yuming .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2018,

[47] The Dirichlet problem for nonlocal elliptic equations [J].

Tian, Rongrong ;

Wei, Jinlong ;

Tang, Yanbin .

APPLICABLE ANALYSIS, 2021, 100 (10) :2093-2107

[48] ON THE EXTERIOR DIRICHLET PROBLEM FOR HESSIAN EQUATIONS [J].

Bao, Jiguang ;

Li, Haigang ;

Li, Yanyan .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 366 (12) :6183-6200

[49] The planar Dirichlet problem for the Stokes equations [J].

Medkova, Dagmar ;

Varnhorn, Werner .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2011, 34 (09) :1097-1109

[50] Topological invariants for the scalar curvature problem on manifolds [J].

Abdullah, Khadijah ;

Chtioui, Hichem .

ADVANCES IN PURE AND APPLIED MATHEMATICS, 2023, 14 (02) :31-47

← 1 2 3 4 5 →