A "milder" version of Calderón's inverse problem for anisotropic conductivities and partial data
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | OUHABAZ, El Maati | |
| dc.date.accessioned | 2024-04-04T03:14:55Z | |
| dc.date.available | 2024-04-04T03:14:55Z | |
| dc.date.created | 2015-01-23 | |
| dc.date.issued | 2018-12-31 | |
| dc.identifier.issn | 1664-039X | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194108 | |
| dc.description.abstractEn | Given a general symmetric elliptic operator $$ L_{a} := \sum_{k,,j=1}^d \p_k (a_{kj} \p_j ) + \sum_{k=1}^d a_k \p_k - \p_k( \overline{a_k} . ) + a_0$$we define the associated Dirichlet-to-Neumann (D-t-N) operator with partial data, i.e., data supported in a part of the boundary. We prove positivity, $L^p$-estimates and domination properties for the semigroup associated with this D-t-N operator. Given $L_a $ and $L_b$ of the previous type with bounded measurable coefficients $a = \{ a_{kj}, \ a_k, a_0 \}$ and $b = \{ b_{kj}, \ b_k, b_0 \}$, we prove that if their partial D-t-N operators (with $a_0$ and $b_0$ replaced by $a_0 -\la$ and $b_0 -\la$) coincide for all $\la$, then the operators $L_a$ and $L_b$, endowed with Dirichlet, mixed or Robin boundary conditions are unitary equivalent. In the case of the Dirichlet boundary conditions, this result was proved recently by Behrndt and Rohleder \cite{BR12} for Lipschitz continuous coefficients. We provide a different proof which works for bounded measurable coefficients and other boundary conditions. | |
| dc.description.sponsorship | Aux frontières de l'analyse Harmonique - ANR-12-BS01-0013 | |
| dc.language.iso | en | |
| dc.publisher | European Mathematical Society | |
| dc.title.en | A "milder" version of Calderón's inverse problem for anisotropic conductivities and partial data | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Mathématiques [math]/Théorie spectrale [math.SP] | |
| dc.identifier.arxiv | 1501.07364 | |
| bordeaux.journal | Journal of Spectral Theory | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01110656 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01110656v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Spectral%20Theory&rft.date=2018-12-31&rft.eissn=1664-039X&rft.issn=1664-039X&rft.au=OUHABAZ,%20El%20Maati&rft.genre=article |
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