# Calder\'on's problem for some classes of conductivities in circularly symmetric domains

## TL;DR

This paper addresses Calderón's inverse conductivity problem in circularly symmetric domains, providing explicit reconstruction formulas and demonstrating Lipschitz stability of the solution.

## Contribution

The paper introduces explicit formulas for conductivity reconstruction in symmetric domains and proves Lipschitz stability, advancing understanding of inverse problems in these settings.

## Key findings

- Explicit reconstruction formulas derived for symmetric domains
- Lipschitz stability of the conductivity reconstruction established
- Enhanced understanding of Calderón's problem in specific geometries

## Abstract

In this note, we study Calder\'on's problem for certain classes of conductivities in domains with circular symmetry in two and three dimensions. Explicit formulas are obtained for the reconstruction of the conductivity from the Dirichlet-to-Neumann map. As a consequence, we show that the reconstruction is Lipschitz stable.