The optimal shape of a dendrite sealed at both ends
Yannick Privat (2009)
Annales de l'I.H.P. Analyse non linéaire
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Displaying similar documents to “Optimal measures for the fundamental gap of Schrödinger operators”
The optimal shape of a dendrite sealed at both ends
On an optimal shape design problem in conduction
José Carlos Bellido (2006)
ESAIM: Control, Optimisation and Calculus of Variations
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In this paper we analyze a typical shape optimization problem in two-dimensional conductivity. We study relaxation for this problem itself. We also analyze the question of the approximation of this problem by the two-phase optimal design problems obtained when we fill out the holes that we want to design in the original problem by a very poor conductor, that we make to converge to zero.
The eigenvalue problem with conductivity boundary conditions
Dorin Bucur, Ioana Durus, Edouard Oudet (2008)
Control and Cybernetics
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Numerical minimization of eigenmodes of a membrane with respect to the domain
Édouard Oudet (2004)
ESAIM: Control, Optimisation and Calculus of Variations
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In this paper we introduce a numerical approach adapted to the minimization of the eigenmodes of a membrane with respect to the domain. This method is based on the combination of the Level Set method of S. Osher and J.A. Sethian with the relaxed approach. This algorithm enables both changing the topology and working on a fixed regular grid.
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...
On the spectrum of a nonlinear planar problem
Francesca Gladiali, Massimo Grossi (2009)
Annales de l'I.H.P. Analyse non linéaire
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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 -Laplacian system....