Some smoothness results for classical problems in optimal design and applications

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• 作者：Juan Casado-Díaz
• 关键词：Optimal design ; Two ; phase material ; Non ; existence ; Relaxation ; 49J20
• 刊名：Chinese Annals of Mathematics - Series B
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：36
• 期：5
• 页码：703-714
• 全文大小：282 KB
• 参考文献：[1]Allaire, G., Shape Optimization by the Homogenization Method, Springer-Verlag, New York, 2002.View Article
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  [3]Casado-Díaz, J., Couce-Calvo, J. and Martín-Gómez, J. D., Relaxation of a control problem in the coefficients with a functional of quadratic growth in the gradient, SIAM J. Control Optim., 43, 2008, 1428-457.View Article
  [4]Casado-Díaz, J., Smoothness properties for the optimal mixture of two isotropic materials, the compliance and eigenvalue problems, SIAM J. Control Optim., to appear.
  [5]Casado-Díaz, J., Some smoothness results for the optimal design of a two-composite material which minimizes the energy, Calc. Var. PDE, 53, 2015, 649-73.View Article
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  [16]Murat, F. and Tartar L., Calcul des variations et homogénéisation, Les Méthodes de L’homogénéisation: Theorie et Applications en Physique, Eirolles, Paris, 1985, 319-69; English translation: Calculus of variations and homogenization, Topics in the Mathematical Modelling of Composite Materials, F. Murat and L. Tartar (eds.), Birkaüser, Boston, 1998 139-74.
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• 作者单位：Juan Casado-Díaz (1)
  
  1. Dpto. de Ecuaciones Diferenciales y Análisis Numérico, University of Seville, 41012, Sevilla, Spain
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Applications of Mathematics
  Chinese Library of Science
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1860-6261

文摘

The author considers two classical problems in optimal design consisting in maximizing or minimizing the energy corresponding to the mixture of two isotropic materials or two-composite material. These results refer to the smoothness of the optimal solutions. They also apply to the minimization of the first eigenvalue.