Geodesic
Aleksandrov-type estimates for a parabolic Monge-Ampère equation
Electronic Journal of Differential Equations, Tome 2005 (2005).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A classical result of Aleksandrov allows us to estimate the size of a convex function $$\int_{\Omega} \det D^{2}u \, dx less than \infty. $$ 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.
Classification : 35K55, 35B45, 35D99
Keywords: parabolic Monge-Ampère measure, pointwise estimates 
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     author = {Hartenstine, David},
     title = {Aleksandrov-type estimates for a parabolic {Monge-Amp\`ere} equation},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2005},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a54/}
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Hartenstine, David. Aleksandrov-type estimates for a parabolic Monge-Ampère equation. Electronic Journal of Differential Equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a54/