#### Vol. 9, No. 4, 2016

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Some counterexamples to Sobolev regularity for degenerate Monge–Ampère equations

### Connor Mooney

Vol. 9 (2016), No. 4, 881–891
##### Abstract

We construct a counterexample to ${W}^{2,1}$ regularity for convex solutions to

in two dimensions. We also prove a result on the propagation of singularities of the form $|{x}_{2}|∕|log{x}_{2}|$ in two dimensions. This generalizes a classical result of Alexandrov and is optimal by example.

##### Keywords
degenerate Monge–Ampère, Sobolev regularity
##### Mathematical Subject Classification 2010
Primary: 35B65, 35J96