Approximation of variational problems with a convexity constraint by PDEs of Abreu type

Abstract : Motivated by some variational problems subject to a convexity constraint, we consider an approximation using the logarithm of the Hessian determinant as a barrier for the constraint. We show that the minimizer of this penalization can be approached by solving a second boundary value problem for Abreu's equation which is a well-posed nonlinear fourth-order elliptic problem. More interestingly, a similar approximation result holds for the initial constrained variational problem.
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Submitted on : Tuesday, May 29, 2018 - 10:19:24 PM
Last modification on : Friday, April 19, 2019 - 4:54:50 PM
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Guillaume Carlier, Teresa Radice. Approximation of variational problems with a convexity constraint by PDEs of Abreu type. 2018. ⟨hal-01802925⟩

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