Abstract
We present examples to show that the solution u of the Monge-Ampère equation det ( D 2 u ) = f ( x ) \det ({D^2}u) = f(x) , with u = 0 u = 0 on the boundary, may not lie in W 2 , p {W^{2,p}} or in C 1 , α {C^{1,\alpha }} for noncontinuous and positive f ( x ) f(x) and for continuous and nonnegative f ( x ) f(x) .
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