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 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.
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| David Hartenstine |
Department of Mathematics
Western Washington University
516 High Street, Bond Hall 202
Bellingham, WA 98225-9063, USA
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