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.
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.
Erkan Nane, Dongsheng Wu, Yimin Xiao (2012)
ESAIM: Probability and Statistics
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For 0 < ≤ 2 and 0 < < 1, an -time fractional Brownian motion is an iterated process = {() = (()) ≥ 0} obtained by taking a fractional Brownian motion {() ∈ ℝ} with Hurst index 0 < < 1 and replacing the time parameter with a strictly -stable Lévy process {() ≥ 0} in ℝ independent of {() ∈ R}. It is shown that such processes have natural connections to partial differential equations and, when is a stable subordinator, can arise as scaling limit...
Erkan Nane, Dongsheng Wu, Yimin Xiao (2012)
ESAIM: Probability and Statistics
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For 0 < ≤ 2 and 0 < < 1, an -time fractional Brownian motion is an iterated process = {() = (()) ≥ 0} obtained by taking a fractional Brownian motion {() ∈ ℝ} with Hurst index 0 < < 1 and replacing the time parameter with a strictly -stable Lévy process {() ≥ 0} in ℝ independent of {() ∈ R}. It is shown that such processes have natural connections to partial differential equations and, when ...
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...
Serge Dubuc, Issa Kagabo, Patrice Marcotte (2010)
RAIRO - Operations Research
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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....
Luís Balsa Bicho, António Ornelas (2014)
ESAIM: Control, Optimisation and Calculus of Variations
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We prove of vector minimizers () = (||) to multiple integrals ∫ ((), |()|) on a ⊂ ℝ, among the Sobolev functions (·) in + (, ℝ), using a : ℝ×ℝ → [0,∞] with (·) and . Besides such basic hypotheses, (·,·) is assumed to satisfy also...
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....
Jean-Charles Régin, Michel Rueher (2010)
RAIRO - Operations Research
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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...
Jérôme Monnot (2010)
RAIRO - Operations Research
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In this paper, we focus on some specific optimization problems from graph theory, those for which all feasible solutions have an equal size that depends on the instance size. Once having provided a formal definition of this class of problems, we try to extract some of its basic properties; most of these are deduced from the equivalence, under differential approximation, between two versions of a problem which only differ on a linear transformation of their objective functions. This...