Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590379 | Journal of Functional Analysis | 2013 | 25 Pages |
Abstract
In this paper, we establish several geometric properties of boundary sections of convex solutions to the Monge–Ampère equation: the engulfing and separating properties and volume estimates. As applications, we prove a covering lemma of Besicovitch type, a covering theorem and a strong type p–p estimate for the maximal function corresponding to boundary sections. Moreover, we show that the Monge–Ampère setting forms a space of homogeneous type.
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Physical Sciences and Engineering
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