Displaying similar documents to “Optimality conditions and exact solutions of the two-dimensional Monge-Kantorovich problem.”

Characterization of optimal shapes and masses through Monge-Kantorovich equation

Guy Bouchitté, Giuseppe Buttazzo (2001)

Journal of the European Mathematical Society

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We study some problems of optimal distribution of masses, and we show that they can be characterized by a suitable Monge-Kantorovich equation. In the case of scalar state functions, we show the equivalence with a mass transport problem, emphasizing its geometrical approach through geodesics. The case of elasticity, where the state function is vector valued, is also considered. In both cases some examples are presented.

Transport problems and disintegration maps

Luca Granieri, Francesco Maddalena (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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By disintegration of transport plans it is introduced the notion of transport class. This allows to consider the Monge problem as a particular case of the Kantorovich transport problem, once a transport class is fixed. The transport problem constrained to a fixed transport class is equivalent to an abstract Monge problem over a Wasserstein space of probability measures. Concerning solvability of this kind of constrained problems, it turns out that in some sense the Monge problem corresponds...

Matrix inequalities and the complex Monge-Ampère operator

Jonas Wiklund (2004)

Annales Polonici Mathematici

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We study two known theorems regarding Hermitian matrices: Bellman's principle and Hadamard's theorem. Then we apply them to problems for the complex Monge-Ampère operator. We use Bellman's principle and the theory for plurisubharmonic functions of finite energy to prove a version of subadditivity for the complex Monge-Ampère operator. Then we show how Hadamard's theorem can be extended to polyradial plurisubharmonic functions.

Finite element approximations of the three dimensional Monge-Ampère equation

Susanne Cecelia Brenner, Michael Neilan (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper, we construct and analyze finite element methods for the three dimensional Monge-Ampère equation. We derive methods using the Lagrange finite element space such that the resulting discrete linearizations are symmetric and stable. With this in hand, we then prove the well-posedness of the method, as well as derive quasi-optimal error estimates. We also present some numerical experiments that back up the theoretical findings. ...