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Some counterexamples to
Sobolev regularity for degenerate Monge–Ampère equations
Connor Mooney |
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Vol. 9 (2016), No. 4, 881–891
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Abstract |
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We construct a counterexample to regularity for convex solutions to in two dimensions. We also prove a result on the propagation of singularities of the form in two dimensions. This generalizes a classical result of Alexandrov and is optimal by example. |
Keywords
degenerate Monge–Ampère, Sobolev regularity
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Mathematical Subject Classification 2010
Primary: 35B65, 35J96
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Milestones
Received: 23 September 2015
Accepted: 11 March 2016
Published: 3 July 2016
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Authors |
| Connor Mooney | |
| Department of Mathematics University of Texas at Austin Austin, TX 78712 United States |
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