Editing Shape optimization (section)

==Examples==
{{Unordered list
|Among all three-dimensional shapes of given volume, find the one which has minimal surface area. Here: 
:<math>\mathcal{F}(\Omega)=\mbox{Area}(\partial \Omega)</math>, 
with 
:<math>\mathcal{G}(\Omega)=\mbox{Volume}(\Omega)=\mbox{const.}</math> 
The answer, given by the [[isoperimetric inequality]], is a [[ball (mathematics)|ball]]. 
|Find the shape of an airplane wing which minimizes [[Drag (physics)|drag]]. Here the constraints could be the wing strength, or the wing dimensions.
|Find the shape of various mechanical structures, which can resist a given [[Stress (physics)|stress]] while having a minimal mass/volume. 
|Given a known three-dimensional object with a fixed radiation source inside, deduce the shape and size of the source based on measurements done on part of the boundary of the object. A formulation of this [[inverse problem]] using [[least-squares]] fit leads to a shape optimization problem.
}}