On the Dirichlet problem for general augmented Hessian equations

被引：18

作者：

Jiang, Feida ^{[1
]}

Trudinger, Neil S. ^{[2
,3
]}

机构：

[1] Nanjing Univ Informat Sci & Technol, Coll Math & Stat, Nanjing 210044, Peoples R China

[2] Australian Natl Univ, Ctr Math & Its Applicat, Canberra, ACT 0200, Australia

[3] Univ Wollongong, Sch Math & Appl Stat, Wollongong, NSW 2522, Australia

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2020年 / 269卷 / 06期

基金：

中国国家自然科学基金; 澳大利亚研究理事会;

关键词：

Dirichlet problem; Augmented Hessian equations; Second derivative estimates; Regular matrix; BOUNDARY-VALUE-PROBLEMS; OPTIMAL TRANSPORTATION; ELLIPTIC-EQUATIONS; REGULARITY;

D O I：

10.1016/j.jde.2020.04.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we apply various first and second derivative estimates and barrier constructions from our treatment of oblique boundary value problems for augmented Hessian equations, to the case of Dirichlet boundary conditions. As a result we extend our previous results on the Monge-Ampere and k-Hessian cases to general classes of augmented Hessian equations in Euclidean space. (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：5204 / 5227

页数：24

共 29 条

[1] 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

[2]

Gilbarg D., 2001, ELLIPTIC PARTIAL DIF

[3] THE DIRICHLET PROBLEM FOR A CLASS OF FULLY NONLINEAR ELLIPTIC-EQUATIONS [J].

GUAN, B .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1994, 19 (3-4) :399-416

[4] Second order estimates for Hessian type fully nonlinear elliptic equations on Riemannian manifolds [J].

Guan, Bo ;

Jiao, Heming .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2015, 54 (03) :2693-2712

[5] THE DIRICHLET PROBLEM FOR HESSIAN TYPE ELLIPTIC EQUATIONS ON RIEMANNIAN MANIFOLDS [J].

Guan, Bo ;

Jiao, Heming .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2016, 36 (02) :701-714

[6] SECOND-ORDER ESTIMATES AND REGULARITY FOR FULLY NONLINEAR ELLIPTIC EQUATIONS ON RIEMANNIAN MANIFOLDS [J].

Guan, Bo .

DUKE MATHEMATICAL JOURNAL, 2014, 163 (08) :1491-1524

[7] Boundary C2,α estimates for Monge-Ampere type equations [J].

Huang, Yong ;

Jiang, Feida ;

Liu, Jiakun .

ADVANCES IN MATHEMATICS, 2015, 281 :706-733

[8]

Ivochkina N., 2004, COMMUN PART DIFF EQ, V26, P859

[9]

Ivochkina N.M., 1991, Leningrad Math. J., V2, P631

[10] The Gårding cones in the modern theory of fully nonlinear second order differential equations [J].

N. M. Ivochkina ;

S. I. Prokof’eva ;

G. V. Yakunina .

Journal of Mathematical Sciences, 2012, 184 (3) :295-315

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