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On singular strictly convex solutions to the Monge-Amp\`ere equation
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classification
math.AP
keywords
convexfunctionmonge-ampsingularstrictlyanswersassociatedequation
abstract
We show the existence of a strictly convex function $u: B_1 \to \mathbb{R}$ with associated Monge-Amp\`ere measure represented by a function $f$ with $0 < f < 1$ a.e. whose Hessian has a singular part. This extends the work [13] and answers an open question of [14,Sec. 6.2(1)].
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