相关论文: Exterior Nonlocal Variational Inequalities

We provide a suitable variational approach for a class of nonlocal problems involving the fractional laplacian and singular nonlinearities for which the standard techniques fail. As a corollary we deduce a characterization of the solutions.

We here establish the higher fractional differentiability for solutions to a class of obstacle problems with non-standard growth conditions. We deal with the case in which the solutions to the obstacle problems satisfy a variational…

We consider the variational inequality problem over the intersection of fixed point sets of firmly nonexpansive operators. In order to solve the problem, we present an algorithm and subsequently show the strong convergence of the generated…

We study the obstacle problem related to a wide class of nonlinear integro-differential operators, whose model is the fractional subLaplacian in the Heisenberg group. We prove both the existence and uniqueness of the solution, and that…

In this paper we study the obstacle problems for the fractional Lapalcian of order $s\in(0,1)$ in a bounded domain $\Omega\subset\mathbb R^n$, under mild assumptions on the data.

The quasi-variational inequalities play a significant role in analyzing a wide range of real-world problems. However, these problems are more complicated to solve than variational inequalities as the constraint set is based on the current…

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…

We determine the asymptotic behaviour of (bilateral) obstacle problems for fractional energies in rather general aperiodic settings via Gamma-convergence arguments. As further developments we consider obstacles with random sizes and shapes…

We prove a uniqueness theorem for the obstacle problem for linear equations involving the fractional Laplacian with zero Dirichlet exterior condition. The problem under consideration arises as the limit of some logistic-type equations. Our…

In this present paper, we introduce and study a dynamical systems involving fractional derivative operator and nonlocal condition, which is constituted of a fractional evolution equation and a time-dependent variational inequality, and is…

In this paper, we consider a rather general linear evolution equation of fractional type, namely a diffusion type problem in which the diffusion operator is the $s$th power of a positive definite operator having a discrete spectrum in…

Now a final and maybe simplest formulation of the enclosure method applied to inverse obstacle problems governed by partial differential equations in a {\it spacial domain with an outer boundary} over a finite time interval is fixed. The…

We present a series of recent results on some new classes of free boundary problems. Differently from the classical literature, the problems considered have either a "nonlocal" feature (e.g., the interaction or/and the interfacial energy…

This survey on stationary and evolutionary problems with gradient constraints is based on developments of monotonicity and compactness methods applied to large classes of scalar and vectorial solutions to variational and quasi-variational…

In this manuscript we deal with existence/uniqueness and regularity issues of suitable weak solutions to nonlocal problems driven by fractional Laplace type operators. Different from previous researches, in our approach we consider gradient…

In this note, we give a brief overview of obstacle problems for nonlocal operators, focusing on the applications to financial mathematics. The class of nonlocal operators that we consider can be viewed as infinitesimal generators of…

The usual treatment of a (first order) classical field theory such as electromagnetism has a little drawback: It has a primary constraint submanifold that arise from the fact that the dynamics is governed by the antisymmetric part of the…

The similarity of feature representations plays a pivotal role in the success of problems related to domain adaptation. Feature similarity includes both the invariance of marginal distributions and the closeness of conditional distributions…

The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example,…

By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…