Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.08662 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- For a compact Riemannian surface $(M,g)$ with non-empty boundary $Γ$, the Dirichlet-to-Neumann operator (DtN-map) $Λ_g:C^\infty(Γ)\to C^\infty(Γ)$ is defined by $Λ_gf=\left.\frac{\partial u}{\partialν}\right|_Γ$, where $ν$ is the unit outer normal vector to the boundary and $u$ is the solution to the Dirichlet problem $Δ_gu=0,\ u|_Γ=f$. The Calderón problem consists of recovering a Riemannian surface from its DtN-map. It is well known that $(M,g)$ is determined by $Λ_g$ uniquely up to a conformal equivalence. We suggest a method for numerical solution of the Calderón problem. The method works well at least for Riemannian surfaces $(M,g)$ close to $({D},e)$, where ${D}=\{(x,y)\mid x^2+y^2\le1\}$ is the unit disk and $e=dx^2+dy^2$ is the Euclidean metric. Our numerical examples confirm the statement: the DtN-map is very sensitive to small deviations of the shape of a domain.