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dc.contributor.author
Fernández-Real, Xavier
dc.contributor.supervisor
Figalli, Alessio
dc.contributor.supervisor
Cabré, Xavier
dc.date.accessioned
2020-10-12T07:27:45Z
dc.date.available
2020-10-10T11:54:37Z
dc.date.available
2020-10-12T07:27:45Z
dc.date.issued
2020
dc.identifier.uri
http://hdl.handle.net/20.500.11850/445413
dc.identifier.doi
10.3929/ethz-b-000445413
dc.description.abstract
The goal of this PhD thesis is to collect the results of the author in the study of thin obstacle problems. We start by giving an introduction to the Signorini or thin obsta\-cle problem, summarizing some of the most relevant currently known results. The next chapters correspond each to one paper by the author (and collaborators). Thus, we start by studying the regularity of solutions for the fully nonlinear thin obstacle problem, to then move to the study of the free boundary for general fractional obstacle problems with drift, in the critical regime. This is followed by a regularity result for minimizers of the perimeter with lower dimensional obstacles. Finally, the last two chapters focus on the standard thin obstacle problem (and its fractional counter-part) and fine regularity and generic regularity properties for the free boundary.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
ETH Zurich
en_US
dc.rights.uri
http://rightsstatements.org/page/InC-NC/1.0/
dc.subject
obstacle problem
en_US
dc.subject
Thin obstacle problem
en_US
dc.subject
Fractional Laplacian
en_US
dc.subject
Free boundary problems
en_US
dc.title
Regularity Theory for Thin Obstacle Problems
en_US
dc.type
Doctoral Thesis
dc.rights.license
In Copyright - Non-Commercial Use Permitted
dc.date.published
2020-10-12
ethz.size
282 p.
en_US
ethz.code.ddc
DDC - DDC::5 - Science::510 - Mathematics
en_US
ethz.grant
Regularity and Stability in Partial Differential Equations
en_US
ethz.identifier.diss
26807
en_US
ethz.publication.place
Zurich
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::02003 - Mathematik Selbständige Professuren::09565 - Figalli, Alessio / Figalli, Alessio
en_US
ethz.grant.agreementno
721675
ethz.grant.fundername
EC
ethz.grant.funderDoi
10.13039/501100000780
ethz.grant.program
H2020
ethz.date.deposited
2020-10-10T11:54:47Z
ethz.source
FORM
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2020-10-12T07:28:12Z
ethz.rosetta.lastUpdated
2020-10-12T07:28:12Z
ethz.rosetta.versionExported
true
ethz.COinS
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