Displaying similar documents to “Optimal multiphase transportation with prescribed momentum”

On optimal matching measures for matching problems related to the Euclidean distance

José Manuel Mazón, Julio Daniel Rossi, Julián Toledo (2014)

Mathematica Bohemica

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We deal with an optimal matching problem, that is, we want to transport two measures to a given place (the target set) where they will match, minimizing the total transport cost that in our case is given by the sum of two different multiples of the Euclidean distance that each measure is transported. We show that such a problem has a solution with an optimal matching measure supported in the target set. This result can be proved by an approximation procedure using a p -Laplacian system....

Optimal transportation for the determinant

Guillaume Carlier, Bruno Nazaret (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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Among ℝ 3 -valued triples of random vectors having fixed marginal probability laws, what is the best way to jointly draw in such a way that the simplex generated by has maximal average volume? Motivated by this simple question, we study optimal transportation problems with several marginals when the objective function is the determinant or its absolute value.

Some remarks on existence results for optimal boundary control problems

Pablo Pedregal (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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An optimal control problem when controls act on the boundary can also be understood as a variational principle under differential constraints and no restrictions on boundary and/or initial values. From this perspective, some existence theorems can be proved when cost functionals depend on the gradient of the state. We treat the case of elliptic and non-elliptic second order state laws only in the two-dimensional situation. Our results are based on deep facts about gradient Young measures. ...

Numerical resolution of an “unbalanced” mass transport problem

Jean-David Benamou (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We introduce a modification of the Monge–Kantorovitch problem of exponent 2 which accommodates non balanced initial and final densities. The augmented lagrangian numerical method introduced in [6] is adapted to this “unbalanced” problem. We illustrate the usability of this method on an idealized error estimation problem in meteorology.

Relaxation of an optimal design problem in fracture mechanic: the anti-plane case

Arnaud Münch, Pablo Pedregal (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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In the framework of the linear fracture theory, a commonly-used tool to describe the smooth evolution of a crack embedded in a bounded domain Ω is the so-called energy release rate defined as the variation of the mechanical energy with respect to the crack dimension. Precisely, the well-known Griffith's criterion postulates the evolution of the crack if this rate reaches a critical value. In this work, in the anti-plane scalar case, we consider the shape design problem which consists...

Vector variational problems and applications to optimal design

Pablo Pedregal (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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We examine how the use of typical techniques from non-convex vector variational problems can help in understanding optimal design problems in conductivity. After describing the main ideas of the underlying analysis and providing some standard material in an attempt to make the exposition self-contained, we show how those ideas apply to a typical optimal desing problem with two different conducting materials. Then we examine the equivalent relaxed formulation to end up with a new problem...