Displaying similar documents to “Distance between components in optimal design problems with perimeter penalization”

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...

Optimal transportation networks as free Dirichlet regions for the Monge-Kantorovich problem

Giuseppe Buttazzo, Eugene Stepanov (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In the paper the problem of constructing an optimal urban transportation network in a city with given densities of population and of workplaces is studied. The network is modeled by a closed connected set of assigned length, while the optimality condition consists in minimizing the Monge-Kantorovich functional representing the total transportation cost. The cost of trasporting a unit mass between two points is assumed to be proportional to the distance between them when the transportation...

A variational model for urban planning with traffic congestion

Guillaume Carlier, Filippo Santambrogio (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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We propose a variational model to describe the optimal distributions of residents and services in an urban area. The functional to be minimized involves an overall transportation cost taking into account congestion effects and two aditional terms which penalize concentration of residents and dispersion of services. We study regularity properties of the minimizers and treat in details some examples.

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....

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...