Stable and periodic solutions to nonlinear equations with fractional diffusion

View/Open
Document typeMaster thesis
Date2016-07
Rights accessOpen Access
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 $n \leq 8$.
DegreeMÀSTER UNIVERSITARI EN MATEMÀTICA AVANÇADA I ENGINYERIA MATEMÀTICA (Pla 2010)
Files | Description | Size | Format | View |
---|---|---|---|---|
memoria.pdf | 499,0Kb | View/Open |