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A liouville theorem for indefinite fractional diffusion equations and its application to existence of solutions
(American Institute of Mathematical Sciences, 2017-11)
In this work we obtain a Liouville theorem for positive, bounded solutions of the equation where (-δ)s stands for the fractional Laplacian with s 2 (0; 1), and the functions h and f are nondecreasing. The main feature is ...
Finite Element Approximation for the Fractional Eigenvalue Problem
(Springer/Plenum Publishers, 2018-10)
The purpose of this work is to study a finite element method for finding solutions to the eigenvalue problem for the fractional Laplacian. We prove that the discrete eigenvalue problem converges to the continuous one and ...
Finite element approximations of the nonhomogeneous fractional Dirichlet problem
(Oxford University Press, 2018-05)
We study finite element approximations of the nonhomogeneous Dirichlet problem for the fractional Laplacian. Our approach is based on weak imposition of the Dirichlet condition and incorporating a nonlocal analogue of the ...
Approximation of solutions of fractional diffusions in compact metric measure spaces
(Birkhauser Verlag Ag, 2017-12)
In this note we prove that the solutions to diffusions associated with fractional powers of the Laplacian in compact metric measure spaces can be obtained as limits of the solutions to particular rescalings of some non-local ...
Fractional Laplacians And Extension Problems: The Higher Rank Case
(2018)
The aim of this paper is to define conformal operators that arise from an extension problem of codimension two. To this end we interpret and extend results of representation theory from a purely analytic point of view. The ...
Global Bifurcation for Fractional p-Laplacian and an Application
(2016)
We prove the existence of an unbounded branch of solutions to the non-linear non-local equation (-Delta)(p)(s)u = lambda vertical bar u vertical bar(p-2)u + f(x, u, lambda) in Omega, u = 0 on R-n \ Omega, bifurcating from ...
A Hopf's lemma and a strong minimum principle for the fractional p-Laplacian
(2017)
Our propose here is to provide a Hopf lemma and a strong minimum principle for weak supersolutions of , (-Delta(p))(s) u = c(x)vertical bar u vertical bar(p-2)u in Omega ,where SI is an open set of R-N, s is an element of ...