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Fractional Sobolev spaces with variable exponents and fractional p(X)-Laplacians
(Univ Szeged, 2017-11)
In this article we extend the Sobolev spaces with variable exponents to include the fractional case, and we prove a compact embedding theorem of these spaces into variable exponent Lebesgue spaces. As an application we ...
Global bifurcation for fractional p-Laplacian and an application
(Heldermann Verlag, 2016-04)
We prove the existence of an unbounded branch of solutions to the nonlinear non-local equation (Equation presented) bifurcating from the first eigenvalue. Here (-Δ)s p denotes the fractional p-Laplacian and Ω ⊂ ℝ1 is a ...
A Hopf's lemma and a strong minimum principle for the fractional p-Laplacian
(Academic Press Inc Elsevier Science, 2017-03-03)
Our propose here is to provide a Hopf lemma and a strong minimum principle for weak supersolutions of (−Δp)su=c(x)|u|p−2u in Ω where Ω is an open set of RN, s∈(0,1), p∈(1,+∞), c∈C(Ω‾) and (−Δp)s is the fractional p-Laplacian.
Multiplicity Results for the Fractional Laplacian in Expanding Domains
(2018-06-01)
In this paper, we establish a multiplicity result of nontrivial weak solutions for the problem (- Δ) αu+ u= h(u) in Ω λ, u= 0 on ∂Ω λ, where Ω λ= λΩ , Ω is a smooth and bounded domain in RN, N> 2 α, λ is a positive parameter, ...
Eigenvalues homogenization for the fractional p-laplacian
(Texas State University. Department of Mathematics, 2016-12)
In this work we study the homogenization for eigenvalues of the fractional p-Laplace operator in a bounded domain both with Dirichlet and Neumann conditions. We obtain the convergence of eigenvalues and the explicit order ...
Non-resonant Fredholm alternative and anti-maximum principle for the fractional p-Laplacian
(Springer, 2017-03)
In this paper we extend two nowadays classical results to a nonlinear Dirichlet problem to equations involving the fractional p-Laplacian. The first result is an existence in a non-resonant range more specific between the ...
The first non-zero Neumann p-fractional eigenvalue
(Pergamon-Elsevier Science Ltd, 2015-01)
In this work we study the asymptotic behavior of the first non-zero Neumann p-fractional eigenvalue λ1(s,p) as s → 1- and as p → ∞. We show that there exists a constant K such that K(1-s)λ1(s,p) goes to the first non-zero ...
A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian
(Pergamon-Elsevier Science Ltd, 2017-08)
In Acosta etal. (2017), a complete n-dimensional finite element analysis of the homogeneous Dirichlet problem associated to a fractional Laplacian was presented. Here we provide a comprehensive and simple 2D MATLAB ® finite ...
Large solutions to elliptic equations involving fractional Laplacian
(Elsevier, 2015)
The purpose of this paper is to study boundary blow up solutions for semi-linear fractional elliptic equations of the form
{(-Delta)(alpha)u(x) + vertical bar u vertical bar(p-1)u(x) = f(x), x is an element of Omega, ...
Improvement of Besov regularity for solutions of the fractional Laplacian
(Springer, 2014-08)
We prove a mean value formula for weak solutions of div(|y| agradu) = 0 in Rn+1 = {(x, y) : x ∈ Rn, y ∈ R}, −1 < a < 1, and balls centered at points of the form (x, 0). We obtain an explicit nonlocal kernel for the mean ...