### A semilinear control problem involving homogenization.

Conca, Carlos, Osses, Axel, Saint Jean Paulin, Jeannine (2001)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Conca, Carlos, Osses, Axel, Saint Jean Paulin, Jeannine (2001)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Tomáš Roubíček (1997)

Commentationes Mathematicae Universitatis Carolinae

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The Young measures, used widely for relaxation of various optimization problems, can be naturally understood as certain functionals on suitable space of integrands, which allows readily various generalizations. The paper is focused on such functionals which can be attained by sequences whose “energy” (=$p$th power) does not concentrate in the sense that it is relatively weakly compact in ${L}^{1}\left(\Omega \right)$. Straightforward applications to coercive optimization problems are briefly outlined.

Ciro D&amp;#039;Apice, Umberto De Maio, Peter I. Kogut (2008)

Annales de l'I.H.P. Analyse non linéaire

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Luciano Carbone, Doina Cioranescu, Riccardo De Arcangelis, Antonio Gaudiello (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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The paper is a continuation of a previous work of the same authors dealing with homogenization processes for some energies of integral type arising in the modeling of rubber-like elastomers. The previous paper took into account the general case of the homogenization of energies in presence of pointwise oscillating constraints on the admissible deformations. In the present paper homogenization processes are treated in the particular case of fixed constraints set, in which minimal coerciveness...

Andrea Braides, Irene Fonseca, Giovanni Leoni (2000)

ESAIM: Control, Optimisation and Calculus of Variations

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Grégoire Allaire, Sergio Gutiérrez (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper is concerned with optimal design problems with a special assumption on the coefficients of the state equation. Namely we assume that the variations of these coefficients have a small amplitude. Then, making an asymptotic expansion up to second order with respect to the aspect ratio of the coefficients allows us to greatly simplify the optimal design problem. By using the notion of -measures we are able to prove general existence theorems for small amplitude optimal design...