The Dirichlet problem for a class of Hessian type equations

被引：1

作者：

Jiao, Heming ^{[1
]}

Wang, Tingting ^{[2
]}

机构：

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

[2] Jiuquan Satellite Launch Ctr, Jiuquan 735000, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2017年 / 453卷 / 01期

关键词：

Hessian type equations; Interior second order estimates; Classical solutions; 2ND-ORDER ELLIPTIC-EQUATIONS; RIEMANNIAN-MANIFOLDS;

D O I：

10.1016/j.jmaa.2017.04.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We are concerned with the Dirichlet problem for a class of Hessian type equations. Applying some new methods we are able to establish the C-2 estimates for an approximating problem under essentially optimal structure conditions. Based on these estimates, the existence of classical solutions is proved. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：509 / 528

页数：20

共 17 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]

EVANS LC, 1982, COMMUN PUR APPL MATH, V35, P334

[3]

GILBARG D., 2015, Elliptic Partial Differential Equations of Second Order

[4]

GUAN B, ARXIV14032133

[5]

Guan B., 2009, INT MATH RES NOT IMR, V2009

[6] Conformal metrics with prescribed curvature functions on manifolds with boundary [J].

Guan, Bo .

AMERICAN JOURNAL OF MATHEMATICS, 2007, 129 (04) :915-942

[7] ON ESTIMATES FOR FULLY NONLINEAR PARABOLIC EQUATIONS ON RIEMANNIAN MANIFOLDS [J].

Guan, Bo ;

Shi, Shujun ;

Sui, Zhenan .

ANALYSIS & PDE, 2015, 8 (05) :1145-1164

[8] 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

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

Guan, Bo .

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

[10] On the Dirichlet problem for degenerate Monge-Ampere equations [J].

Guan, PF ;

Trudinger, NS ;

Wang, XJ .

ACTA MATHEMATICA, 1999, 182 (01) :87-104

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