On a class of inverse electrostatic and elasticity problems
  We study the inverse electrostatic and elasticity problems associated with Poisson and Navier equations. The uniqueness of solutions of these problems is proved for piecewise constant electric charge and internal stress distributions having a checkered structure: they are constant on rectangular blocks. Such distributions appear naturally in practical applications. We also discuss computational challenges arising in the numerical implementation of our method. 
Andrei Artemev, Leonid Parnovski and Iosif Polterovich
math.AP math-ph math.MP