A localization theorem and boundary regularity for a class of degenerate Monge-Ampere equations

作者：Savin Ovidiu^*

来源：Journal of Differential Equations, 2014, 256(2): 327-388.

DOI：10.1016/j.jde.2013.08.019

We consider degenerate Monge Ampere equations of the type
det D(2)u = f in Omega, f similar to d(partial derivative Omega)(alpha) near partial derivative Omega,
where d(partial derivative Omega) represents the distance to the boundary of the domain Omega and alpha > 0 is a positive power. We obtain C-2 estimates at the boundary under natural conditions on the boundary data and the right-hand side. Similar estimates in two dimensions were obtained by J.X. Hong, G. Huang and W. Wang in [3].

• 出版日期2014-1-15