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Stable and periodic solutions to nonlinear equations with fractional diffusion

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Sanz Perela, TomásMés informacióMés informació
Tutor / directorCabré Vilagut, XavierMés informacióMés informacióMés informació
Document typeMaster thesis
Date2016-07
Rights accessOpen Access
Attribution-NonCommercial-NoDerivs 3.0 Spain
Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain
Abstract
The aim of this thesis is to study stable solutions to nonlinear elliptic equations involving the fractional Lapacian. More precisely, we study the extremal solution for the problem $(\Delta )^s u = \lambda f(u)$ in $\Omega$, $u \equiv 0 $ in $\R^n \setminus \Omega$, where $\lambda > 0$ is a parameter and $s \in (0,1)$. The main result of this work, which is new, is the following: we prove that when $s=1/2$ and $\Omega = B_1$, then the extremal solution is bounded whenever $n \leq 8$.
SubjectsDifferential equations, Partial, Equacions en derivades parcials
DegreeMÀSTER UNIVERSITARI EN MATEMÀTICA AVANÇADA I ENGINYERIA MATEMÀTICA (Pla 2010)
URIhttp://hdl.handle.net/2117/89944
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  • Màsters oficials - Master of Science in Advanced Mathematics and Mathematical Engineering (MAMME) [242]
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