相关论文: Exterior Nonlocal Variational Inequalities
This paper is concerned with a new type of inverse obstacle problem governed by a variable-order time-fraction diffusion equation in a bounded domain. The unknown obstacle is a region where the space dependent variable-order of fractional…
In this paper, we consider a class of variational problems with integral functionals involving nonlocal gradients. These models have been recently proposed as refinements of classical hyperelasticity, aiming for an effective framework to…
We investigate the obstacle problem for a class of nonlinear equations driven by nonlocal, possibly degenerate, integro-differential operators, whose model is the fractional $p$-Laplacian operator with measurable coefficients. Amongst other…
This paper is concerned with analyzing a class of fractional calculus of variations problems and their associated Euler-Lagrange (fractional differential) equations. Unlike the existing fractional calculus of variations which is based on…
Very recently M. Warma has shown that for nonlocal PDEs associated with the fractional Laplacian, the classical notion of controllability from the boundary does not make sense and therefore it must be replaced by a control that is localized…
In this article we present the first results on domain decomposition methods for nonlocal operators. We present a nonlocal variational formulation for these operators and establish the well-posedness of associated boundary value problems,…
Based on the mathematical-physical model of pavement mechanics, a multilayer elastic system with interlayer friction conditions is constructed. Given the complex boundary conditions, the corresponding variational inequalities of the partial…
We show global uniqueness in an inverse problem for the fractional Schr\"odinger equation: an unknown potential in a bounded domain is uniquely determined by exterior measurements of solutions. We also show global uniqueness in the partial…
This work concerns with the existence of solutions for the following class of nonlocal elliptic problems \begin{equation*}\label{00} \left\{ \begin{array}{l} (-\Delta)^{s}u + u = |u|^{p-2}u\;\;\mbox{in $\Omega$},\\ u \geq 0 \quad \mbox{in}…
We study cohomological obstructions to the existence of global conserved quantities. In particular, we show that, if a given local variational problem is supposed to admit global solutions, certain cohomology classes cannot appear as…
We consider linear and obstacle problems driven by a nonlocal integral operator, for which nonlocal interactions are restricted to a ball of finite radius. These type of operators are used to model anomalous diffusion and, for a special…
We present a systematic study on a class of nonlocal integral functionals for functions defined on a bounded domain and the naturally induced function spaces. The function spaces are equipped with a seminorm depending on finite differences…
The abstract elliptic and parabolic equations on exterior domain are considered. The equations have top-order variable coefficients. The separability properties of boundary value problems for elliptic equation and well-posedness of the…
Variational inequalities are an important mathematical tool for modelling free boundary problems that arise in different application areas. Due to the intricate nonsmooth structure of the resulting models, their analysis and optimization is…
The center of interest in this work are variational problems with integral functionals depending on special nonlocal gradients. The latter correspond to truncated versions of the Riesz fractional gradient, as introduced in [Bellido, Cueto &…
We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem in perforated domains.
We provide a short introduction of new and well-known facts relating non-local operators and irregular domains. Cauchy problems and boundary value problems are considered in case non-local operators are involved. Such problems respectively…
Variational-hemivariational inequalities are an area full of interesting and challenging mathematical problems. The area can be viewed as a natural extension of that of variational inequalities. Variational-hemivariational inequalities are…
Motivated by problems in machine learning, we study a class of variational problems characterized by nonlocal operators. These operators are characterized by power-type weights, which are singular at a portion of the boundary. We identify a…
We consider the fractional generalization of nonholonomic constraints defined by equations with fractional derivatives and provide some examples. The corresponding equations of motion are derived using variational principle.