Volume 16, Issue 4
A Review of Theoretical Measure Approaches in Optimal Shape Problems

Alireza Fakharzadeh Jahromi & Hajar Alimorad

DOI:

Int. J. Numer. Anal. Mod., 16 (2019), pp. 543-574.

Published online: 2019-02

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  • Abstract

Some optimal shape design problems lack classical solutions, or at least, the existence of such solutions is far from being straightforward. In such cases, to obtain an optimal solution, a variety of methods have been employed. In this study, we review the works that used measures which can basically be divided in two groups: using Young measures and embedding process (Shape-measure method). We also survey the advantages and disadvantages of these two methods and investigate their improved version in the presented works and applications.

  • Keywords

Young measure, radon measure, atomic measure, optimal shape, shape-measure, linear programming problem, relaxed problem.

  • AMS Subject Headings

49M20, 49J20, 90C90, 49M25

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

a_fakharzadeh@sutech.ac.ir (Alireza Fakharzadeh Jahromi)

hajaralimorad@yahoo.com (Hajar Alimorad)

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