# On Jörgens, Calabi, and Pogorelov type theorem and isolated singularities of parabolic Monge–Ampère equations

@article{Xiong2011OnJC, title={On J{\"o}rgens, Calabi, and Pogorelov type theorem and isolated singularities of parabolic Monge–Amp{\`e}re equations}, author={Jingang Xiong and Jiguang Bao}, journal={Journal of Differential Equations}, year={2011}, volume={250}, pages={367-385} }

## 20 Citations

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

- Mathematics
- 2018

AbstractWe extend a theorem of Jörgens, Calabi and Pogorelov on entire solutions of elliptic Monge–Ampère equation to parabolic Monge–Ampère equation, and obtain delicate asymptotic behavior of…

Symmetry of solutions to parabolic Monge-Ampère equations

- Mathematics
- 2013

AbstractIn this paper, we study the parabolic Monge-Ampère equation
−utdet(D2u)=f(t,u)in Ω×(0,T].
Using the method of moving planes, we show that any parabolically convex solution is symmetric with…

A Calabi theorem for solutions to the parabolic Monge–Ampère equation with periodic data

- MathematicsAnnales de l'Institut Henri Poincaré C, Analyse non linéaire
- 2018

Ancient solutions of exterior problem of parabolic Monge–Ampère equations

- MathematicsAnnali di Matematica Pura ed Applicata (1923 -)
- 2020

We use Perron method to prove the existence of ancient solutions of exterior problem for a kind of parabolic Monge–Ampere equation
$$-\,u_t\det D^2u=f$$
with prescribed asymptotic behavior at…

Multi-valued solutions to a class of parabolic Monge-Ampèreequations

- Mathematics
- 2013

In this paper, we investigate the multi-valued solutions of a class
of parabolic Monge-Ampere equation $-u_{t}\det(D^{2}u)=f$. Using
the Perron method, we obtain the existence of finitely valued…

Entire Solutions of Cauchy Problem for Parabolic Monge–Ampère Equations

- MathematicsAdvanced Nonlinear Studies
- 2020

Abstract In this paper, we study the Cauchy problem of the parabolic Monge–Ampère equation - u t det D 2 u = f ( x , t ) -u_{t}\det D^{2}u=f(x,t) and obtain the existence and uniqueness of…

Existence of multi-valued solutions with asymptotic behavior of parabolic Monge-Ampère equation

- Mathematics
- 2015

In this paper, we extend the results of multi-valued solutions of elliptic Monge-Ampère equation to parabolic Monge-Ampère equation. We use the Perron method to prove the existence of multi-valued…

A Pogorelov estimate and a Liouville-type theorem to parabolic k-Hessian equations

- MathematicsCommunications in Contemporary Mathematics
- 2019

We consider Pogorelov estimates and Liouville-type theorems to parabolic [Formula: see text]-Hessian equations of the form [Formula: see text] in [Formula: see text]. We derive that any [Formula: see…

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