A Generalization of a Theorem by Calabi to the Parabolic Monge-Ampère Equation
Document Type
Article
Publication Date
1-1-1998
Identifier/URL
40983513 (Pure)
Abstract
We prove that if the function u = u(x,t), convex in x and nonincreasing in t, has time derivative bounded away from 0 and −∞, and is a solution of the parabolic Monge-Ampère equation $-u_{t} \text{det} D^{2}_{x} u = 1$ in ℝn × (−∞,0], then u must be of the form a convex quadratic polynomial in x plus a linear function of t.
Repository Citation
Gutiérrez, C. E.,
& Huang, Q.
(1998). A Generalization of a Theorem by Calabi to the Parabolic Monge-Ampère Equation. Indiana University Mathematics Journal, 47 (4), 1459-1479.
https://corescholar.libraries.wright.edu/math/510
DOI
10.1512/iumj.1998.47.1563
