Some smoothness results for the optimal design of a two-composite material which minimizes the energy

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• 作者：Juan Casado-Díaz
• 关键词：49N60 ; 49J20
• 刊名：Calculus of Variations and Partial Differential Equations
• 出版年：2015
• 出版时间：July 2015
• 年：2015
• 卷：53
• 期：3-4
• 页码：649-673
• 全文大小：601 KB
• 参考文献：1.Allaire, G.: Shape Optimization by the Homogenization Method. Appl. Math. Sci., vol. 146. Springer, New York (2002)
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  4.Casado-Díaz, J.: Smoothness properties for the optimal mixture of two isotropic materials. The compliance and eigenvalue problems (to appear)
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• 作者单位：Juan Casado-Díaz (1)
  
  1. Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, C. Tarfía s/n, 41012, Sevilla, Spain
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Systems Theory and Control
  Calculus of Variations and Optimal Control
  Mathematical and Computational Physics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0835

文摘

We study the smoothness properties of the optimal solutions corresponding to the minimization of the potential energy for the mixture of two isotropic materials (electric, thermic, elastic membrane,\(\ldots \)). As it is well known this problem has not solution in general and therefore our results refer to a relaxed formulation. We show that the state function \(u\) is twice derivable and that the optimal proportion is derivable in the direction of \(\nabla u\). We also get some uniqueness results and applications to the non-existence of classical (unrelaxed) solutions.