A remark on precomposition on $\sH^{1/2}(S^1)$ and $\eps$-identifiability of disks in tomography
| dc.creator | Dambrine, Marc | |
| dc.creator | Kateb, Djalil | |
| dc.date | 2006-07-07 | |
| dc.date.accessioned | 2026-07-07T07:39:42Z | |
| dc.date.available | 2026-07-07T07:39:42Z | |
| dc.description | We consider the inverse conductivity problem with one measurement for the equation $div((σ\_1+(σ\_2-σ\_1)χ\_D)\nabla{u})=0$ determining the unknown inclusion $D$ included in $Ω$. We suppose that $Ω$ is the unit disk of $\mathbb{R}^2$. With the tools of the conformal mappings, of elementary Fourier analysis and also the action of some quasi-conformal mapping on the Sobolev space $\sH^{1/2}(S^1)$, we show how to approximate the Dirichlet-to-Neumann map when the original inclusion $D$ is a $ε-$ approximation of a disk. This enables us to give some uniqueness and stability results. | |
| dc.identifier | https://arxiv.org/abs/math/0607205 | |
| dc.identifier | http://arxiv.org/abs/math/0607205 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121548 | |
| dc.subject | Optimization and Control | |
| dc.subject | 34K29, 42A16, 46E35 | |
| dc.title | A remark on precomposition on $\sH^{1/2}(S^1)$ and $\eps$-identifiability of disks in tomography | |
| dc.type | text |