# Reconstruction of domains with algebraic boundaries from generalized polarization tensors

## TL;DR

This paper demonstrates the stability of reconstructing smooth planar domains with algebraic boundaries using a finite set of generalized polarization tensors, extending previous work to less regular domains.

## Contribution

It introduces a stable recovery method for algebraic boundary domains from polarization tensors without regularity assumptions, building on prior theoretical identification of boundary-defining polynomials.

## Key findings

- Recovery procedure is stable and effective for domains with algebraic boundaries.
- No regularity assumptions are needed for the domain in the reconstruction process.
- Performance and limitations of the method are demonstrated through examples.

## Abstract

This paper aims at showing the stability of the recovery of a smooth planar domain with a real algebraic boundary from a finite number of its generalized polarization tensors. It is a follow-up of the work [H. Ammari et al., Math. Annalen, 2018], where it is proved that the minimal polynomial with real coefficients vanishing on the boundary can be identified as the generator of a one dimensional kernel of a matrix whose entries are obtained from a finite number of generalized polarization tensors. The recovery procedure is implemented without any assumption on the regularity of the domain to be reconstructed and its performance and limitations are illustrated.