Wednesday, October 3, 2012

1210.0124 (Andrei Artemev et al.)

Inverse problems for Poisson and Navier equations    [PDF]

Andrei Artemev, Leonid Parnovski, Iosif Polterovich
We formulate and study the inverse electrostatics and elasticity problems associated with Poisson and Navier equations. Necessary and sufficient conditions for the uniqueness of solutions of these inverse problems are discussed. In particular, the uniqueness of solutions is proved for some classes of electric charge and internal stress distributions that appear naturally in practical applications. We also construct a family of distributions for which the uniqueness property fails, and discuss computational challenges arising in the numerical implementation of our method.
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