Aleksandrov-type estimates for a parabolic Monge-Ampere equation
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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 det D2u 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.
CitationHartenstine, D. (2005). Aleksandrov-type estimates for a parabolic Monge-Ampere equation. Electronic Journal of Differential Equations, 2005(11), pp. 1-8.
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