Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 11, pp. 1-8.

Title: Aleksandrov-type estimates for a parabolic Monge-Ampere equation

Author: David Hartenstine (Western Washington Univ., Bellingham, WA, USA)

Abstract: 
  A classical result of Aleksandrov allows us to estimate the size of
  a convex function $u$ at a point $x$ in a bounded domain $\Omega$
  in terms of the distance from $x$ to the boundary of $\Omega$ if
  $\int_{\Omega} \det D^{2}u \, dx < \infty$.  This estimate plays a
  prominent role in the existence and regularity theory of the
  Monge-Ampere equation.  Jerison proved an extension of Aleksandrov's
  result that provides a similar estimate, in some cases for which this
  integral is infinite.  Gutierrez and Huang proved a variant of
  the Aleksandrov estimate, relevant to solutions of a parabolic
  Monge-Ampere equation.  In this paper, we prove Jerison-like
  extensions to this parabolic estimate.
 
Submitted January 12, 2005. Published January 27, 2005.
Math Subject Classifications: 35K55, 35B45, 35D99.
Key Words: Parabolic Monge-Ampere measure; pointwise estimates.