Displaying similar documents to “Global minimizer of the ground state for two phase conductors in low contrast regime”

Convex shape optimization for the least biharmonic Steklov eigenvalue

Pedro Ricardo Simão Antunes, Filippo Gazzola (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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The least Steklov eigenvalue for the biharmonic operator in bounded domains gives a bound for the positivity preserving property for the hinged plate problem, appears as a norm of a suitable trace operator, and gives the optimal constant to estimate the -norm of harmonic functions. These applications suggest to address the problem of minimizing in suitable classes of domains. We survey the existing results and conjectures about this topic;...

On shape optimization problems involving the fractional laplacian

Anne-Laure Dalibard, David Gérard-Varet (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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Our concern is the computation of optimal shapes in problems involving (−). We focus on the energy (Ω) associated to the solution of the basic Dirichlet problem ( − )  = 1 in Ω,  = 0 in Ω. We show that regular minimizers Ω of this energy under a volume constraint are disks. Our proof goes through the explicit computation of the shape derivative (that seems to be completely new in the fractional context), and a refined adaptation of the...

Relating phase field and sharp interface approaches to structural topology optimization

Luise Blank, Harald Garcke, M. Hassan Farshbaf-Shaker, Vanessa Styles (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. We also discuss how to deal with triple junctions where two materials and the void meet. Finally, we present several numerical results for...

Un algorithme d'identification de frontières soumises à des conditions aux limites de Signorini

Slim Chaabane, Mohamed Jaoua (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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This work deals with a non linear inverse problem of reconstructing an unknown boundary , the boundary conditions prescribed on being of Signorini type, by using boundary measurements. The problem is turned into an optimal shape design one, by constructing a Kohn & Vogelius-like cost function, the only minimum of which is proved to be the unknown boundary. Furthermore, we prove that the derivative of this cost function with respect to a direction depends only on the state ...

On torsional rigidity and principal frequencies: an invitation to the Kohler−Jobin rearrangement technique

Lorenzo Brasco (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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We generalize to the -Laplacian a spectral inequality proved by M.-T. Kohler−Jobin. As a particular case of such a generalization, we obtain a sharp lower bound on the first Dirichlet eigenvalue of of a set in terms of its -torsional rigidity. The result is valid in every space dimension, for every 1    ∞ and for every open set with finite measure. Moreover, it holds by replacing the first eigenvalue with more general optimal Poincaré-Sobolev constants....

Asymptotic behaviour and numerical approximation of optimal eigenvalues of the Robin laplacian

Pedro Ricardo Simão Antunes, Pedro Freitas, James Bernard Kennedy (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the problem of minimising the th-eigenvalue of the Robin Laplacian in R. Although for  = 1,2 and a positive boundary parameter it is known that the minimisers do not depend on , we demonstrate numerically that this will not always be the case and illustrate how the optimiser will depend on . We derive a Wolf–Keller type result for this problem and show that optimal eigenvalues grow at most with , which is in sharp contrast with the Weyl asymptotics for a...

Design-dependent loads in topology optimization

Blaise Bourdin, Antonin Chambolle (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We present, analyze, and implement a new method for the design of the stiffest structure subject to a pressure load or a given field of internal forces. Our structure is represented as a subset  of a reference domain, and the complement of is made of two other “phases”, the “void” and a fictitious “liquid” that exerts a pressure force on its interface with the solid structure. The problem we consider is to minimize the compliance of the structure , which is the total work of...

Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1

Tiziana Durante, Taras A. Mel’nyk (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider quasilinear optimal control problems involving a thick two-level junction which consists of the junction body and a large number of thin cylinders with the cross-section of order 𝒪( ). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. In addition, the quasilinear boundary...

Shape optimization problems for metric graphs

Giuseppe Buttazzo, Berardo Ruffini, Bozhidar Velichkov (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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): ∈ 𝒜, ℋ() = }, where ℋ ,,  }  ⊂ R . The cost functional ℰ() is the Dirichlet energy of defined through the Sobolev functions on vanishing on the points . We analyze the existence of a solution in both the families of connected sets and of metric graphs. At the end, several explicit examples are discussed.

Minimising convex combinations of low eigenvalues

Mette Iversen, Dario Mazzoleni (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the variational problem         inf{ () +  () + (1 −  − ) () | Ω open in ℝ, || ≤ 1}, for  ∈ [0, 1],  +  ≤ 1, where () is the th eigenvalue of the Dirichlet Laplacian acting in () and || is the Lebesgue measure of . We investigate for which values of every minimiser is connected.

Bottleneck Capacity Expansion Problems with General Budget Constraints

Rainer E. Burkard, Bettina Klinz, Jianzhong Zhang (2010)

RAIRO - Operations Research

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This paper presents a unified approach for bottleneck capacity expansion problems. In the bottleneck capacity expansion problem, BCEP, we are given a finite ground set , a family of feasible subsets of and a nonnegative real capacity ĉ for all . Moreover, we are given monotone increasing cost functions for increasing the capacity of the elements as well as a budget . The task is to determine new capacities c ≥ ĉ such that the objective function given by...

A non elliptic spectral problem related to the analysis of superconducting micro-strip lines

Anne-Sophie Bonnet-Bendhia, Karim Ramdani (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper is devoted to the spectral analysis of a non elliptic operator , deriving from the study of superconducting micro-strip lines. Once a sufficient condition for the self-adjointness of operator has been derived, we determine its continuous spectrum. Then, we show that is unbounded from below and that it has a sequence of negative eigenvalues tending to -∞. Using the Min-Max principle, a characterization of its positive eigenvalues is given. Thanks to this characterization,...

Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1

Tiziana Durante, Taras A. Mel’nyk (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We consider quasilinear optimal control problems involving a thick two-level junction which consists of the junction body and a large number of thin cylinders with the cross-section of order 𝒪( ). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. ...

Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1

Tiziana Durante, Taras A. Mel’nyk (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We consider quasilinear optimal control problems involving a thick two-level junction which consists of the junction body and a large number of thin cylinders with the cross-section of order 𝒪( ). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. ...