Related papers: Fractional De Giorgi classes and applications to n…

We study energy functionals obtained by adding a possibly discontinuous potential to an interaction term modeled upon a Gagliardo-type fractional seminorm. We prove that minimizers of such non-differentiable functionals are locally bounded,…

In the past years, the phenomenon of fractional regularity has been addressed for a large class of linear and/or quasilinear differential operators, mostly, in terms of certain Besov spaces. As it turned out, for equations governed by the…

The study of nonlocal operators of fractional type possesses a long tradition, motivated both by mathematical curiosity and by real world applications...

This article is dedicated to the proof of the existence of classical solutions for a class of non-linear integral variational problems. Those problems are involved in nonlocal image and signal processing.

We consider the fractional Laplace framework and provide models and theorems related to nonlocal diffusion phenomena. Some applications are presented, including: a simple probabilistic interpretation, water waves, crystal dislocations,…

In this paper, a class of nonlocal fractional Dirichlet problems is studied. By using a variational principle due to Ricceri (whose original version was given in J. Comput. Appl. Math. 113 (2000), 401-410), the existence of infinitely many…

The purpose of this paper is to study the existence of (weak) periodic solutions for nonlocal fractional equations with periodic boundary conditions. These equations have a variational structure and, by applying a critical point result…

We present an extension of the classical De Giorgi class, and then we show that functions in this new class are locally bounded and locally H\"older continuous. Some applications are given. As a first application, we give a regularity…

We study robust regularity estimates for local minimizers of nonlocal functionals with non-standard growth of $(p,q)$-type and for weak solutions to a related class of nonlocal equations. The main results of this paper are local boundedness…

We give an alternative proof for H\"older regularity for weak solutions of nonlocal elliptic quasilinear equations modelled on the fractional p-Laplacian where we replace the discrete De Giorgi iteration on a sequence of concentric balls by…

We deal with the De Giorgi H{\"o}lder regularity theory for parabolic equations with rough coefficients and parabolic De Giorgi classes which extend the notion of solution. We give a quantitative proof of the interior H{\"o}lder regularity…

We study the local behavior of the elements of a specific energy class of functions, called the nonlocal parabolic ($p$-homogenous) De Giorgi class. First we carry on an analysis of their local boundedness under optimal tail conditions, and…

We study regularity for a parabolic problem with fractional diffusion in space and a fractional time derivative. Our main result is a De Giorgi-Nash-Moser Holder regularity theorem for solutions in a divergence form equation. We also prove…

In this paper the generalisation of previous author's formulation of fractional continuum mechanics to the case of anisotropic non-locality is presented. The considerations include the review of competitive formulations available in…

We overview some recent existence and regularity results in the theory of nonlocal nonlinear problems driven by the fractional $p$-Laplacian.

The aim of this study to investigate the existence of solutions for the following nonlocal integral boundary value problem of Caputo type fractional differential inclusions. To achieve our goals, we take advantage of fixed point theorems…

In this review article we present regularity properties of generalized functions which are useful in the analysis of non-linear problems. It is shown that Schwartz distributions embedded into our new spaces of generalized functions, with…

We establish the density of the partial regularity result in the class of continuous viscosity solutions. Given a fully nonlinear equation, we prove the existence of a sequence entitled to the partial regularity result, approximating its…

In this work we wish to highlight some consequences of a recent result proved in [N. D. Cong and H. T. Tuan, Generation of nonlocal fractional dynamical systems by fractional differential equations, J. Integral Equations Appl. 29 (2017),…

We derive some regularity estimates of the solution to a time fractional diffusion equation, that are useful for numerical analysis, and partially unravel the singularity structure of the solution with respect to the time variable.