We present nonlocal algorithms for video denoising, simplification and inpainting based on a generic framework of discrete regularization on graphs. We express video denoising, simplification and inpainting problems using the same variational formulation. The main advantage of this framework is the unification of local and nonlocal approaches for these processing procedures. We take advantage o...

Fractional differential equations arise in many engineering and scientific disciplines as the mathematical modeling of systems and processes in various fields, such as physics,mechanics, chemical technology, population dynamics, biotechnology, and economics (see, e.g., [1–7]). As one of the important topics in the research on differential equations, the boundary value problem has attained a gre...

Well-posedness results for the state-based peridynamic nonlocal continuum model of solid mechanics are established with the help of a nonlocal vector calculus. The peridynamic strain energy density for an elastic constitutively linear anisotropic heterogenous solid is expressed in terms of the field operators of that calculus, after which a variational principle for the equilibrium state is def...

We propose two algorithms based on Bregman iteration and operator splitting technique for nonlocal TV regularization problems. The convergence of the algorithms is analyzed and applications to deconvolution and sparse reconstruction are presented.

In this article, using the sub-supersolution method and Rabinowitztype global bifurcation theory, we prove some results on existence, uniqueness and multiplicity of positive solutions for some singular nonlocal elliptic problems.

‎This paper gives an abstract order-type existence theorem for second order nonlocal boundary value problems at resonance and obtain existence criteria for at least two positive solutions‎, ‎where $f$ is a continuous function‎. ‎Our results generalize or extend related results in the literature and give a positive answer to the question raised in the literature‎. ‎An example is given to illustr...

Torsional dynamic analysis of carbon nanotubes under the effect of longitudinal magnetic field is carried out in the present study. Torque effect of an axial magnetic field on a carbon nanotube has been defined using Maxwell’s relation. Nonlocal governing equation and boundary conditions for carbon nanotubes are obtained by using Hamilton’s minimum energy principle. Eringen’s nonlocal stress gr...

We consider coarsening in interfacial systems driven by nonlocal energies. Of particular interest are the nonlocal Cahn–Hilliard equation and models of biological aggregation. The energies considered cause the system to separate into phases. The pattern of interfaces evolves under nonlocal surfacetension-type effects. The typical length scales grow and the pattern coarsens. We prove a rigorous ...

and Applied Analysis 3 He studied the asymptotic behavior of solutions and found the influence of weight function on the existence of global and blow-up solutions. Wang et al. 10 studied porous medium equation with power form source term ut Δu u, x, t ∈ Ω × 0, ∞ , 1.8 subjected to nonlocal boundary condition 1.2 . By virtue of the method of upper-lower solutions, they obtained global existence,...

In this paper using a fixed point theory on a cone we present some new results on the existence of multiple positive solutions for singular nonlocal boundary value problems involving integral conditions with derivative dependence.