Stability Estimates for Coefficients of Magnetic Schrödinger Equation From Full and Partial Boundary Measurements
| dc.creator | Tzou, Leo | |
| dc.date | 2006-02-07 | |
| dc.date.accessioned | 2026-07-07T07:03:13Z | |
| dc.date.available | 2026-07-07T07:03:13Z | |
| dc.description | In this paper we establish a $log log$-type estimate which shows that in dimension $n\geq 3$ the magnetic field and the electric potential of the magnetic Schrödinger equation depends stably on the Dirichlet to Neumann (DN) map even when the boundary measurement is taken only on a subset that is slightly larger than half of the boundary $\partialΩ$. Furthermore, we prove that in the case when the measurement is taken on all of $\partialΩ$ one can establish a better estimate that is of $log$-type. The proofs involve the use of the complex geometric optics (CGO) solutions of the magnetic Schrödinger equation constructed in \cite{sun uhlmann} then follow a similar line of argument as in \cite{alessandrini}. In the partial data estimate we follow the general strategy of \cite{hw} by using the Carleman estimate established in \cite{FKSU} and a continuous dependence result for analytic continuation developed in \cite{vessella}. | |
| dc.identifier | https://arxiv.org/abs/math/0602147 | |
| dc.identifier | http://arxiv.org/abs/math/0602147 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/108888 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Stability Estimates for Coefficients of Magnetic Schrödinger Equation From Full and Partial Boundary Measurements | |
| dc.type | text |