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A Liouville type result for fractional Schrödinger operators in 1D

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Felipe Navarro, Juan CarlosMés informació
Tutor / directorCabré Vilagut, XavierMés informacióMés informacióMés informació
Document typeMaster thesis
Date2017-01
Rights accessOpen Access
Attribution-NonCommercial-ShareAlike 3.0 Spain
Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-ShareAlike 3.0 Spain
Abstract
The 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.
SubjectsDifferential equations, Partial, Equacions en derivades parcials
DegreeMÀSTER UNIVERSITARI EN MATEMÀTICA AVANÇADA I ENGINYERIA MATEMÀTICA (Pla 2010)
URIhttp://hdl.handle.net/2117/100464
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  • Màsters oficials - Master of Science in Advanced Mathematics and Mathematical Engineering (MAMME) [264]
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