In this work we deal with the Dirichlet homogeneous problem for the integral fractional Laplacian on a bounded domain Ω ⊂ R. Namely, we deal with basic analytical aspects required to convey a complete Finite Element analysis of the problem (1) { (−∆)u = f in Ω, u = 0 in Ω, where the fractional Laplacian of order s is defined by (−∆)u(x) = C(n, s) P.V. ∫ Rnu(x)− u(y)|x− y|n+2s dyand ...

This paper concerns the study of asymptotic behavior solutions to a family fractional type problems on bounded domain, satisfying homogeneous Dirichlet boundary conditions. The differential operators includes $$p_n$$ -Laplacian when $$p_n\rightarrow \infty $$ as particular case, tough it could be extended function Hölder quotient order s, whose primitive is an Orlicz appropriated growth limit e...

Invariance is an attractive principle for specifying image processing algorithms. In this presentation, we promote affine invariance—more precisely, invariance with respect to translation, scaling and rotation. As starting point, we identify the corresponding class of invariant 2D operators: these are combinations of the (fractional) Laplacian and the complex gradient (or Wirtinger operator). W...

The long-term limit motions of individual heavy-tailed (power-law) particle jumps that characterize anomalous diffusion may have different scaling rates in different directions. Operator stable motions [Y(t):t> or =0] are limits of d-dimensional random jumps that are scale-invariant according to c(H)Y(t)=Y(ct), where H is a dxd matrix. The eigenvalues of the matrix have real parts 1/alpha(j), w...

We derive exact form of the piecewise-linear finite element stiffness matrix on general non-uniform meshes for integral fractional Laplacian operator in one dimension, where derivation is accomplished Fourier transformed space. With such an formulation at our disposal, we are able to numerically study some intrinsic properties commonly used (e.g., graded mesh), particular, examine their seamles...

In this paper, we study the effect of Hardy potential on existence or non-existence solutions to a fractional Laplacian problem involving singular nonlinearity. Also, mention stability result.