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Lotka-Volterra models with fractional diffusion
(Cambridge Univ Press, 2017-06-01)
We study Lotka-Volterra models with fractional Laplacian. To do this we study in detail the logistic problem and show that the sub-supersolution method works for both the scalar problem and for systems. We apply this method ...
Regularity theory and high order numerical methods for the (1D)-fractional Laplacian
(American Mathematical Society, 2017-03)
This paper presents regularity results and associated high-order numerical methods for one-dimensional Fractional-Laplacian boundary-value problems. On the basis of a factorization of solutions as a product of a certain ...
Optimal partition problems for the fractional Laplacian
(Springer Heidelberg, 2018-04)
In this work, we prove an existence result for an optimal partition problem of the form min{Fs(A1, …, Am) : Ai ∈ As, Ai ∩ Aj = ∅ for i ≠ j}, where Fs is a cost functional with suitable assumptions of monotonicity and lower ...
General types of spherical mean operators and k-functionals of fractional orders
(AIMSSpringfield, 2015-05)
We design a general type of spherical mean operators and employ them to approximate 'L IND.P' class functions. We show that optimal orders of approximation are achieved via appropriately defined K-functionals of fractional orders.
Self-generated interior blow-up solutions in fractional elliptic equation with absorption
(2015)
In this paper, we study positive solutions to problems involving the fractional Laplacian
{(-Delta)(alpha)u(x) + vertical bar u vertical bar(p-1)u(x) = 0, x is an element of Omega \ C,
u(x) = 0, x is an element of ...
Non-local Diffusion Equations Involving the Fractional p(·) -Laplacian
(2019-01-01)
In this paper we study a class of nonlinear quasi-linear diffusion equations involving the fractional p(·) -Laplacian with variable exponents, which is a fractional version of the nonhomogeneous p(·) -Laplace operator. The ...
A fractional Laplace equation: Regularity of solutions and finite element approximations
(Society for Industrial and Applied Mathematics, 2017-01)
This paper deals with the integral version of the Dirichlet homogeneous fractional Laplace equation. For this problem weighted and fractional Sobolev a priori estimates are provided in terms of the Holder regularity of the ...
The obstacle problem for the infinity fractional laplacian
(Springer, 2016-11)
Given g an α-H¨older continuous function defined on the boundary of a bounded domain Ω and given ψ a continuous obstacle defined in Ω, in this article, we find u an α-H¨older extension of g in Ω with u ≥ ψ. This function ...
H-convergence result for nonlocal elliptic-type problems via tartar's method
(Society for Industrial and Applied Mathematics, 2017-07)
In this work we obtain a compactness result for the H-convergence of a family of nonlocal and nonlinear monotone elliptic-type problems by means of Tartar's method of oscillating test functions.
Infinitely Many Solutions For A Critical Kirchhoff Type Problem Involving A Fractional Operator
(KHAYYAM PUBL CO INCATHENS, 2016)