A Comparison Principle for Parabolic Complex Monge-Ampere Equations

被引：0

作者：

Do, Hoang-Son ^{[1
]}

Thanh Cong Ngoc Pham ^{[2
]}

机构：

[1] Vietnam Acad Sci & Technol, Inst Math, 18 Hoang Quoc Viet, Hanoi, Vietnam

[2] VNU Univ Sci, Dept Math, 334 Nguyen Trai, Hanoi, Vietnam

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2022年 / 32卷 / 01期

关键词：

Viscosity solutions; Parabolic Monge-Ampere equation; Pluripotential theory; VISCOSITY SOLUTIONS; FLOWS;

D O I：

10.1007/s12220-021-00748-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the Cauchy-Dirichlet problem for parabolic complex Monge-Ampere equations on strongly pseudoconvex domains using the viscosity method. We prove a comparison principle for parabolic complex Monge-Ampere equations and use it to study the existence and uniqueness of viscosity solution in certain cases where the sets {z is an element of Omega : f(t, z) = 0} may be pairwise disjoint.

引用

页数：19

共 50 条

[21] A VARIATIONAL APPROACH TO COMPLEX MONGE-AMPERE EQUATIONS
Berman, Robert J.
Boucksom, Sebastien
Guedj, Vincent
Zeriahi, Ahmed
PUBLICATIONS MATHEMATIQUES DE L IHES, 2013, (117): : 179 - 245
[22] Weak subsolutions to complex Monge-Ampere equations
Guedj, Vincent
Lu, Chinh H.
Zeriahi, Ahmed
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2019, 71 (03) : 727 - 738
[23] ON THE NEUMANN PROBLEMS FOR COMPLEX MONGE-AMPERE EQUATIONS
LI, SY
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1994, 43 (04) : 1099 - 1122
[24] Geometric estimates for complex Monge-Ampere equations
Fu, Xin
Guo, Bin
Song, Jian
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2020, 765 : 69 - 99
[25] Weak Solution of Parabolic Complex Monge-Ampere Equation
Do Hoang Son
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2017, 66 (06) : 1949 - 1979
[26] Ancient solutions of exterior problem of parabolic Monge-Ampere equations
Zhou, Ziwei
Gong, Shuyu
Bao, Jiguang
ANNALI DI MATEMATICA PURA ED APPLICATA, 2021, 200 (04) : 1605 - 1624
[27] Exterior problems of parabolic Monge-Ampere equations for n=2
Dai, Limei
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2014, 67 (08) : 1497 - 1506
[28] GEOMETRY OF MONGE-AMPERE EQUATIONS
MORIMOTO, T
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1979, 289 (01): : 25 - 28
[29] A COMPARISON PRINCIPLE FOR THE COMPLEX MONGE-AMPERE OPERATOR IN CEGRELL'S CLASSES AND APPLICATIONS
Nguyen Van Khue
Pham Hoang Hiep
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 361 (10) : 5539 - 5554
[30] Classification of Monge-Ampere Equations
Kushner, Alexei G.
DIFFERENTIAL EQUATIONS: GEOMETRY, SYMMETRIES AND INTEGRABILITY - THE ABEL SYMPOSIUM 2008, 2009, 5 : 223 - 256

← 1 2 3 4 5 →