# On Some Geometric Inverse Problems for Nonscalar Elliptic Systems

## TL;DR

This paper investigates geometric inverse problems for linear elliptic systems, establishing uniqueness and stability results, and exploring how observations vary with domain perturbations, with potential applications in approximation strategies.

## Contribution

It introduces new methods for analyzing inverse problems for elliptic systems using Carleman estimates and domain differentiation techniques.

## Key findings

- Proves uniqueness of solutions for certain inverse problems.
- Establishes stability estimates relating observations to domain changes.
- Suggests a computational approach for approximating inverse solutions.

## Abstract

In this paper, we consider several geometric inverse problems for linear elliptic systems. We prove uniqueness and stability results. In particular, we show the way that the observation depends on the perturbations of the domain. In some particular situations, this provides a strategy that could be used to compute approximations to the solution of the inverse problem. In the proofs, we use techniques related to (local) Carleman estimates and differentiation with respect to the domain.