Displaying similar documents to “Convex shape optimization for the least biharmonic Steklov eigenvalue”

On shape optimization problems involving the fractional laplacian

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

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

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...

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

Similarity:

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...

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

Similarity:

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

Similarity:

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....

Conjugate-cut loci and injectivity domains on two-spheres of revolution

Bernard Bonnard, Jean-Baptiste Caillau, Gabriel Janin (2013)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

In a recent article [B. Bonnard, J.-B. Caillau, R. Sinclair and M. Tanaka, 26 (2009) 1081–1098], we relate the computation of the conjugate and cut loci of a family of metrics on two-spheres of revolution whose polar form is  = d  + ()d to the period mapping of the -variable. One purpose of this article is to use this relation to evaluate the cut and conjugate loci for a family of metrics arising as a deformation of the round sphere and to determine the...

Minimising convex combinations of low eigenvalues

Mette Iversen, Dario Mazzoleni (2014)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

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.

Shape optimization problems for metric graphs

Giuseppe Buttazzo, Berardo Ruffini, Bozhidar Velichkov (2014)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

): ∈ 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.

Inequality-sum: a global constraint capturing the objective function

Jean-Charles Régin, Michel Rueher (2010)

RAIRO - Operations Research

Similarity:

This paper introduces a new method to prune the domains of the variables in constrained optimization problems where the objective function is defined by a sum , and where the integer variables are subject to difference constraints of the form . An important application area where such problems occur is deterministic scheduling with the as optimality criteria. This new constraint is also more general than a sum constraint defined on a set of ordered variables. Classical...

On convex sets that minimize the average distance

Antoine Lemenant, Edoardo Mainini (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

In this paper we study the compact and convex sets K ⊆ Ω ⊆ ℝ2that minimize ∫ Ω ( , K ) d + λ 1 Vol ( K ) + λ 2 Per ( K ) ∫ Ω dist ( x ,K ) d x + λ 1 Vol ( K ) + λ 2 Per ( K ) for some constantsλ 1 and λ 2, that could possibly be zero. We compute in particular the second order derivative of the functional and use...

Undecidability of infinite post correspondence problem for instances of size 8

Jing Dong, Qinghui Liu (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Similarity:

The infinite Post Correspondence Problem (PCP) was shown to be undecidable by Ruohonen (1985) in general. Blondel and Canterini [36 (2003) 231–245] showed that PCP is undecidable for domain alphabets of size 105, Halava and Harju [40 (2006) 551–557] showed that PCP is undecidable for domain alphabets of size 9. By designing a special coding, we delete a letter from Halava and Harju’s construction. So we prove that PCP is undecidable for domain alphabets of size 8.

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. In addition, the quasilinear boundary...

An Extended Opportunity-Based Age Replacement Policy

Bermawi P. Iskandar, Hiroaki Sandoh (2010)

RAIRO - Operations Research

Similarity:

The present study proposes an extended opportunity-based age replacement policy where opportunities occur according to a Poisson process. When the age, of the system satisfies for a prespecified value , a corrective replacement is conducted if the objective system fails. In case satisfies for another prespecified value , we take an opportunity to preventively replace the system by a new one with probability , and do not take the opportunity with probability . At the moment reaches...

Trivial Cases for the Kantorovitch Problem

Serge Dubuc, Issa Kagabo, Patrice Marcotte (2010)

RAIRO - Operations Research

Similarity:

Let and be two compact spaces endowed with respective measures and satisfying the condition . Let be a continuous function on the product space . The mass transfer problem consists in determining a measure on whose marginals coincide with and , and such that the total cost be minimized. We first show that if the cost function is decomposable, i.e., can be represented as the sum of two continuous functions defined on and , respectively, then every feasible measure is optimal....

On indecomposable sets with applications

Andrew Lorent (2014)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

In this note we show the characteristic function of every indecomposable set in the plane is equivalent to the characteristic function a closed set See Formula in PDF See Formula in PDF . We show by example this is false in dimension three and above. As a corollary to this result we show that for every > 0 a set of finite perimeter can be approximated by a closed subset See Formula in PDF See Formula in PDF with finitely many indecomposable components and with the property that...