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Inverse Problems For Third-Order Nonlinear Perturbations Of Biharmonic Operators by Bhattacharyya, Sombuddha; Krupchyk, Katya; Sahoo, Suman Kumar; Uhlmann, Gunther is a scholarly article available to read on EtoBox.

What is Inverse Problems For Third-Order Nonlinear Perturbations Of Biharmonic Operators about?

We study inverse boundary problems for third-order nonlinear tensorial perturbations of biharmonic operators on a bounded domain in $\mathbb{R}^n$, where $n\geq 3$. By imposing appropriate assumptions on the nonlinearity, we demonstrate that the Dirichlet-to-Neumann map, known on the boundary of the domain, uniquely determines the genuinely nonlinear tensorial third-order perturbations of the biharmonic operator. The proof relies on the inversion of certain generalized momentum ray transforms on symmetric tensor fields. Notably, the corresponding inverse boundary problem for linear tensorial third-order perturbations of the biharmonic operator remains an open question.

Author

Bhattacharyya, Sombuddha; Krupchyk, Katya; Sahoo, Suman Kumar; Uhlmann, Gunther

Published

2023

Language

EN