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dc.contributor.author
Railo, Jesse
dc.contributor.author
Zimmermann, Philipp
dc.date.accessioned
2023-09-05T11:33:22Z
dc.date.available
2023-09-03T03:38:48Z
dc.date.available
2023-09-05T11:33:22Z
dc.date.issued
2023-07
dc.identifier.issn
1664-039X
dc.identifier.issn
1664-0403
dc.identifier.other
10.4171/JST/444
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/629415
dc.identifier.doi
10.3929/ethz-b-000629415
dc.description.abstract
We generalize many recent uniqueness results on the fractional Calderón problem to cover the cases of all domains with nonempty exterior. The highlight of our work is the characterization of uniqueness and nonuniqueness of partial data inverse problems for the fractional conductivity equation on domains that are bounded in one direction for conductivities supported in the whole Euclidean space and decaying to a constant background conductivity at infinity. We generalize the uniqueness proof for the fractional Calderón problem by Ghosh, Salo and Uhlmann to a general abstract setting in order to use the full strength of their argument. This allows us to observe that there are also uniqueness results for many inverse problems for higher order local perturbations of a lower order fractional Laplacian. We give concrete example models to illustrate these curious situations and prove Poincaré inequalities for the fractional Laplacians of any order on domains that are bounded in one direction. We establish Runge approximation results in these general settings, improve regularity assumptions also in the cases of bounded sets and prove general exterior determination results. Counterexamples to uniqueness in the inverse fractional conductivity problem with partial data are constructed in another companion work.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
European Mathematical Society
en_US
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
dc.subject
Fractional Laplacian
en_US
dc.subject
fractional gradient
en_US
dc.subject
Calderón problem
en_US
dc.subject
Poincaré inequality
en_US
dc.title
Fractional Calderón problems and Poincaré inequalities on unbounded domains
en_US
dc.type
Journal Article
dc.rights.license
Creative Commons Attribution 4.0 International
dc.date.published
2023-07-28
ethz.journal.title
Journal of Spectral Theory
ethz.journal.volume
13
en_US
ethz.journal.issue
1
en_US
ethz.journal.abbreviated
J. Spectr. Theory
ethz.pages.start
63
en_US
ethz.pages.end
131
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.identifier.wos
ethz.publication.place
Berlin
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02204 - RiskLab / RiskLab
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::09557 - Cheridito, Patrick / Cheridito, Patrick
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02204 - RiskLab / RiskLab
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::09557 - Cheridito, Patrick / Cheridito, Patrick
ethz.date.deposited
2023-09-03T03:38:55Z
ethz.source
WOS
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2023-09-05T11:33:23Z
ethz.rosetta.lastUpdated
2024-02-03T03:17:31Z
ethz.rosetta.versionExported
true
ethz.COinS
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