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On the regularity of the complex Monge-Ampère equations
2012
Proceedings of the American Mathematical Society
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We shall consider the regularity of solutions for the complex Monge-Ampère equations in C n or a bounded domain. First we prove interior C 2 estimates of solutions in a bounded domain for the complex Monge-Ampère equations with the assumption of an L p bound for u, p > n 2 , and of a Lipschitz condition on the right-hand side. Then we shall construct a family of Pogorelov-type examples for the complex Monge-Ampère equations. These examples give generalized entire solutions (as well as viscosity
doi:10.1090/s0002-9939-2011-11178-x
fatcat:2sj4cuddmzdw3lvbcpkrchqdky