Viscosity solutions of general viscous Hamilton-Jacobi equations

被引：36

作者：

Armstrong, Scott N. ^{[1
]}

Tran, Hung V. ^{[2
]}

机构：

[1] Univ Paris 09, CEREMADE, CNRS, UMR 7534, F-75775 Paris, France

[2] Univ Chicago, Dept Math, Chicago, IL 60637 USA

来源：

MATHEMATISCHE ANNALEN | 2015年 / 361卷 / 3-4期

关键词：

PARTIAL-DIFFERENTIAL-EQUATIONS; ELLIPTIC-EQUATIONS; STATE CONSTRAINTS; QUADRATIC GROWTH;

D O I：

10.1007/s00208-014-1088-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present comparison principles, Lipschitz estimates and study state constraints problems for degenerate, second-order Hamilton-Jacobi equations.

引用

页码：647 / 687

页数：41

共 19 条

[1]

Armstrong S.N., ARXIV13101749MATHAP

[2]

Armstrong S.N., COMM PARTIA IN PRESS

[3] Stochastic homogenization of Hamilton-Jacobi and degenerate Bellman equations in unbounded environments [J].

Armstrong, Scott N. ;

Souganidis, Panagiotis E. .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2012, 97 (05) :460-504

[4] On the generalized Dirichlet problem for viscous Hamilton-Jacobi equations [J].

Barles, G ;

Da Lio, F .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2004, 83 (01) :53-75

[5] Uniqueness results for quasilinear parabolic equations through viscosity solutions' methods [J].

Barles, G ;

Biton, S ;

Bourgoing, M ;

Ley, O .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2003, 18 (02) :159-179

[6]

Barles G., 1991, DIFFERENTIAL INTEGRA, V4, P241

[7]

BARLES G, 1987, ESAIM-MATH MODEL NUM, V21, P557

[8] The generalisation of Dirichlet's problem [J].

Bernstein, S .

MATHEMATISCHE ANNALEN, 1910, 69 :82-136

[9] USERS GUIDE TO VISCOSITY SOLUTIONS OF 2ND-ORDER PARTIAL-DIFFERENTIAL EQUATIONS [J].

CRANDALL, MG ;

ISHII, H ;

LIONS, PL .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 27 (01) :1-67

[10] Uniqueness results for second-order Bellman-Isaacs equations under quadratic growth assumptions and applications [J].

Da Lio, F ;

Ley, O .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2006, 45 (01) :74-106

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