We study the inverse electrostatic and elasticity problems associated with Poisson and Navier equations. These problems arise in a number of applications, such as diagnostic of electronic devices and analysis of residual stresses in materials. In microelectronics, piecewise constant distributions of electric charge having a checkered structure (i.e., that are constant on rectangular blocks) are of particular importance. We prove that the inverse electrostatic problem has a unique solution for such distributions. We also show that the inverse elasticity problem has a unique solution for checkered distributions of body forces. General necessary and sufficient conditions for the uniqueness of solutions of both inverse problems are discussed as well.

Inverse Problems
Department of Mechanical and Aerospace Engineering

Artemev, A, Parnovski, L. (Leonid), & Polterovich, I. (Iosif). (2013). Inverse electrostatic and elasticity problems for checkered distributions. Inverse Problems, 29(7). doi:10.1088/0266-5611/29/7/075010