TY - JOUR
T1 - A Review of Theoretical Measure Approaches in Optimal Shape Problems
AU - Jahromi , Alireza Fakharzadeh
AU - Alimorad , Hajar
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 543
EP - 574
PY - 2019
DA - 2019/02
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/13014.html
KW - Young measure, radon measure, atomic measure, optimal shape, shape-measure, linear programming problem, relaxed problem.
AB - <p style="text-align: justify;">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.</p>