Existence of the global solution for the parabolic Monge-Ampère equations on compact Riemannian manifolds

DOI10.1016/j.jmaa.2011.12.005zbMath1237.58027OpenAlexW2019507366WikidataQ115346134 ScholiaQ115346134MaRDI QIDQ663734

Zhiwen Duan, Jianning Huang

Publication date: 27 February 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.12.005

zbMATH Keywords

existencenonexistenceglobal solutionparabolic Monge-Ampère equations

Mathematics Subject Classification ID

Heat and other parabolic equation methods for PDEs on manifolds (58J35) Parabolic Monge-Ampère equations (35K96)

Related Items (2)

A note on the asymptotic behavior of parabolic Monge-Ampère equations on Riemannian manifolds ⋮ Global existence of solutions to parabolic Monge-Ampère equations on Riemannian manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the mean oscillation of the Hessian of solutions to the Monge-Ampère equation
• Existence and non-existence of solutions for a class of Monge-Ampère equations
• Deformation of Kähler metrics to Kähler-Einstein metrics on compact Kähler manifolds
• The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
• Equations du type Monge-Ampère sur les variétés Riemanniennes compactes. I
• Equations du type de Monge-Ampère sur les variétés Riemanniennes compactes. II
• Equations du type de Monge-Ampère sur les variétés Riemanniennes compactes. III
• Boundary-value problems on \(S^ n\) for surfaces of constant Gauss curvature
• Parabolic Monge-Ampère equations on Riemannian manifolds
• A Liouville theorem for solutions of the Monge--Ampère equation with periodic data.
• Monge-Ampère equations on Riemannian manifolds
• Three-manifolds with positive Ricci curvature
• Boundary regularity for the Monge-Ampère and affine maximal surface equations
• Existence and estimates of solutions to a singular Dirichlet problem for the Monge-Ampère equation
• The complex Monge-Ampère equation with infinite boundary value
• Existence of solutions to initial value problem for a parabolic Monge-Ampère equation and application
• Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens
• The Dirichlet problem for the prescribed curvature equations
• On second derivative estimates for equations of Monge-Ampère type
• Some existence results for fully nonlinear elliptic equations of monge-ampère type
• BOUNDEDLY NONHOMOGENEOUS ELLIPTIC AND PARABOLIC EQUATIONS IN A DOMAIN
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• The dirichlet problem for nonlinear second-order elliptic equations. II. Complex monge-ampère, and uniformaly elliptic, equations
• Nonlinear second-order elliptic equations V. The dirichlet problem for weingarten hypersurfaces
• On the regularity of the solution of then-dimensional Minkowski problem
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I

This page was built for publication: Existence of the global solution for the parabolic Monge-Ampère equations on compact Riemannian manifolds