Abstract
n this paper, we consider the following parabolic Monge-Ampère equation
− A(x)ut + ( det D2u)1/n = f (x, t), in Q = Ω × (0, T](1.1)
where <em>u</em>= <em>u</em>(<em>x</em>, <em>t</em>) is convex in <em>x</em> for every 0 < <em>t</em> ≤ T, D<sup>2</sup><em>u</em> denotes the Hessian of <em>u</em> with respect to <em>x</em>, and Ω is a bounded convex domain in R<sup>n</sup>.
− A(x)ut + ( det D2u)1/n = f (x, t), in Q = Ω × (0, T](1.1)
where <em>u</em>= <em>u</em>(<em>x</em>, <em>t</em>) is convex in <em>x</em> for every 0 < <em>t</em> ≤ T, D<sup>2</sup><em>u</em> denotes the Hessian of <em>u</em> with respect to <em>x</em>, and Ω is a bounded convex domain in R<sup>n</sup>.
| Original language | English |
|---|---|
| Pages (from-to) | 453-480 |
| Number of pages | 28 |
| Journal | American Journal of Mathematics |
| Volume | 128 |
| Issue number | 2 |
| DOIs | |
| State | Published - Apr 2006 |
ASJC Scopus Subject Areas
- General Mathematics