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dc.contributorCabré Vilagut, Xavier
dc.contributor.authorFelipe Navarro, Juan Carlos
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2017-02-01T14:25:04Z
dc.date.available2017-02-01T14:25:04Z
dc.date.issued2017-01
dc.identifier.urihttp://hdl.handle.net/2117/100464
dc.description.abstractThe aim of this master's thesis is to obtain an alternative and original proof of a Liouville type result for fractional Schrödinger operators in 1D without using a local extension problem, in the spirit of the recent work of Hamel et al. Thanks to this new proof we can extend the Liouville theorem to other nonlocal operators that do not have a local extension problem, being the first time that a result of this kind is proven. First, we introduce Schrödinger operators, the fractional Laplacian and its local extension problem. Then, we present a recent work about a nonlocal and nonlinear problem, where the prior study of fractional Schrödinger operators is needed. We also present the most important motivation for the study of Liouville type results: the conjecture of De Giorgi, and we review some Liouville type results both with local and nonlocal operators. Finally, we give the proof of the main theorems of the thesis.
dc.language.isoeng
dc.publisherUniversitat Politècnica de Catalunya
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials
dc.subject.lcshDifferential equations, Partial
dc.subject.otherNonlocal equations
dc.subject.otherIntegral operators
dc.subject.otherSchrödinger operator
dc.subject.otherFractional Laplacian
dc.subject.otherLiouville type result
dc.subject.otherDe Giorgi conjecture
dc.titleA Liouville type result for fractional Schrödinger operators in 1D
dc.typeMaster thesis
dc.subject.lemacEquacions en derivades parcials
dc.subject.amsClassificació AMS::35 Partial differential equations::35B Qualitative properties of solutions
dc.identifier.slugFME-1416
dc.rights.accessOpen Access
dc.date.updated2017-01-31T07:08:03Z
dc.audience.educationlevelMàster
dc.audience.mediatorUniversitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística
dc.audience.degreeMÀSTER UNIVERSITARI EN MATEMÀTICA AVANÇADA I ENGINYERIA MATEMÀTICA (Pla 2010)


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