Aleksandrov-type Estimates for a Parabolic Monge-ampère Equation
نویسنده
چکیده
A classical result of Aleksandrov allows us to estimate the size of a convex function u at a point x in a bounded domain Ω in terms of the distance from x to the boundary of Ω if ∫ Ω detD 2u dx < ∞. This estimate plays a prominent role in the existence and regularity theory of the Monge-Ampère equation. Jerison proved an extension of Aleksandrov’s result that provides a similar estimate, in some cases for which this integral is infinite. Gutiérrez and Huang proved a variant of the Aleksandrov estimate, relevant to solutions of a parabolic Monge-Ampère equation. In this paper, we prove Jerison-like extensions to this parabolic estimate.
منابع مشابه
An Aleksandrov-type Estimate for a Parabolic Monge-ampère Equation
A classical result of Aleksandrov allows one to estimate the size of a convex function u at a point x in a bounded domain Ω in terms of the distance from x to the boundary of Ω if R Ω det Du dx < ∞. This estimate plays a prominent role in the existence and regularity theory of the Monge-Ampère equation. Jerison proved an extension of Aleksandrov’s result that provides a similar estimate, in som...
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