An extension of Jörgens-Calabi-Pogorelov theorem to parabolic Monge-Ampère equation

DOI10.1007/s00526-018-1363-5zbMath1391.35250OpenAlexW2802335743WikidataQ115387245 ScholiaQ115387245MaRDI QIDQ1650901

Bo Wang, Wei Zhang, Ji Guang Bao

Publication date: 16 July 2018

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-018-1363-5

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Entire solutions to PDEs (35B08) Parabolic Monge-Ampère equations (35K96) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items

The first initial-boundary value problem of parabolic Monge-Ampère equations outside a bowl-shaped domain ⋮ Entire solutions of Cauchy problem for parabolic Monge-Ampère equations ⋮ Asymptotic mean value formulas for parabolic nonlinear equations ⋮ On the complete solutions to the Tchebychev affine Kähler equation and its geometric significance ⋮ A Pogorelov estimate and a Liouville-type theorem to parabolic k-Hessian equations ⋮ A rigidity theorem for parabolic 2-Hessian equations ⋮ Asymptotic behavior of solutions of Monge-Ampère equations with general perturbations of boundary values ⋮ The Solutions with Prescribed Asymptotic Behavior for the Exterior Dirichlet Problem of Hessian Equations ⋮ Entire solutions to the parabolic Monge-Ampère equation with unbounded nonlinear growth in time ⋮ Parabolic Hessian equations outside a bowl-shaped domain ⋮ Asymptotic behavior of solutions of fully nonlinear equations over exterior domains ⋮ A Liouville theorem of parabolic Monge-Ampère equations in half-space ⋮ The asymptotic behavior of viscosity solutions of Monge-Ampère equations in half space ⋮ On the rigidity theorems for entire Lagrangian translating solitons in pseudo-Euclidean space IV

Cites Work

• Bernstein theorem and regularity for a class of Monge-Ampère equations
• On Jörgens, Calabi, and Pogorelov type theorem and isolated singularities of parabolic Monge-Ampère equations
• A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity
• Differentiation of integrals in \(\mathbb{R}^n\)
• Sequences of convex functions and estimates of the maximum of the solution of a parabolic equation
• A Liouville theorem for solutions of the Monge--Ampère equation with periodic data.
• Regularity results on the parabolic Monge-Ampère equation with \(VMO\) type data
• On the improper convex affine hyperspheres
• Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens
• Über die Lösungen der Differentialgleichung \({r t - s^2 = 1}\)
• On an Aleksandrov-Bakel'Man Type Maximum Principle for Second-Order Parabolic Equations
• Deforming a hypersurface by its Gauss-Kronecker curvature
• Complete affine hypersurfaces. Part I. The completeness of affine metrics
• Shapes of worn stones
• A generalization of a theorem by Calabi to the parabolic Monge-Ampere equation
• An extension to a theorem of Jörgens, Calabi, and Pogorelov
• Geometric properties of the sections of solutions to the Monge-Ampère equation
• \(W^{2,p}\) estimates for the parabolic Monge-Ampère equation
• Some aspects of the global geometry of entire space-like submanifolds
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item