On a class of inverse electrostatic and elasticity problems

TL;DR

This paper investigates the uniqueness of solutions in inverse electrostatic and elasticity problems with piecewise constant distributions, addressing practical applications and computational challenges in numerical methods.

Contribution

It proves uniqueness for piecewise constant distributions with checkered structures and discusses computational challenges in numerical implementation.

Findings

Proved uniqueness for piecewise constant distributions with checkered structure.

Addressed computational challenges in numerical methods.

Applicable to practical inverse electrostatic and elasticity problems.

Abstract

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.