Bounds on the volume fraction of the two-phase shallow shell using one   measurement
  We study the size estimate problem for the two-phase shallow shell equations in this paper. Our aim is to derive bounds on the volume fraction of each phase assuming that the material properties of the two phases are given. The approach in this paper is based on the translation method. One of the key steps is to connect the shallow shell equations to the thin plate equation. 
Hyeonbae Kang, Graeme W. Milton, and Jenn-Nan Wang
math.AP