Electron. J. Diff. Eqns., Vol. 2005(2005), No. 11, pp. 18.
Aleksandrovtype estimates for a parabolic MongeAmpere equation
David Hartenstine
Abstract:
A classical result of Aleksandrov allows us to estimate the size of
a convex function
at a point
in a bounded domain
in terms of the distance from
to the boundary of
if
This estimate plays a
prominent role in the existence and regularity theory of the
MongeAmpere 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
MongeAmpere equation. In this paper, we prove Jerisonlike
extensions to this parabolic estimate.
Submitted January 12, 2005. Published January 27, 2005.
Math Subject Classifications: 35K55, 35B45, 35D99.
Key Words: Parabolic MongeAmpere measure; pointwise estimates.
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David Hartenstine
Department of Mathematics
Western Washington University
516 High Street, Bond Hall 202
Bellingham, WA 982259063, USA
email: david.hartenstine@wwu.edu 
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