相关论文: Bochner formula and Bernstein type estimates on lo…

In this paper authors consider representations of graphs in Hilbert spaces applying a restriction of local scalarity on them. It enables to obtain a theory, similar to the classical theory of representations of graphs in vector spaces. In…

Recently, \citeauthor*{akbari2021locality}~(ICALP 2023) studied the locality of graph problems in distributed, sequential, dynamic, and online settings from a {unified} point of view. They designed a novel $O(\log n)$-locality deterministic…

Graph-based approximation methods are of growing interest in many areas, including transportation, biological and chemical networks, financial models, image processing, network flows, and more. In these applications, often a basis for the…

A nonlocal contact problem for two-dimensional linear elliptic equations is stated and investigated. The method of separation of variables is used to find the solution of a stated problem in case of Poisson's equation. Then the more general…

We start presenting an $L^{\infty}$-gradient bound for solutions to non-homogeneous $p$-Laplacean type systems and equations, via suitable non-linear potentials of the right hand side. Such a bound implies a Lorentz space characterization…

Given a finite Lie incidence geometry which is either a polar space of rank at least $3$ or a strong parapolar space of symplectic rank at least $4$ and diameter at most $4$, or the parapolar space arising from the line Grassmannian of a…

A map from the initial conditions to the values of the function and its first spatial derivative evaluated at the interface is constructed for the heat equation on finite and infinite domains with $n$ interfaces. The existence of this map…

The relationships between eigenvalues and eigenvectors of a product graph and those of its factor graphs have been known for the standard products, while characterization of Laplacian eigenvalues and eigenvectors of the Kronecker product of…

We consider weighted graphs with an infinite set of vertices. We show that boundedness of all functions of finite energy can be seen as a notion of `relative compactness' for such graphs and study sufficient and necessary conditions for…

This paper investigates the gradient flow structure, well-posedness, and asymptotic behavior of the Fokker-Planck equation defined on locally uniformly finite graphs, which is highly non-trivial compared with the finite case. We first…

In this article, we consider nonlocal Hamilton-Jacobi Equations on networks with Kirchhoff type conditions for the interior vertices and Dirichlet boundary conditions for the boundary ones: our aim is to provide general existence and…

A pathwise construction of discontinuous Brownian motions on metric graphs is given for every possible set of non-local Feller-Wentzell boundary conditions. This construction is achieved by locally decomposing the metric graphs into star…

We construct models of exactly solvable two-particle quantum graphs with certain non-local two-particle interactions, establishing appropriate boundary conditions via suitable self-adjoint realisations of the two-particle Laplacian. Showing…

We study the eigenvalues of the connection Laplacian on a graph with an orthogonal group or unitary group signature. We establish higher order Buser type inequalities, i.e., we provide upper bounds for eigenvalues in terms of Cheeger…

In the present paper we study inverse problems related to determining the time-dependent coefficient and unknown source function of fractional heat equations. Our approach shows that having just one set of data at an observation point…

In this thesis, we analyze the stochastic completeness of a heat kernel on graphs which is a function of three variables: a pair of vertices and a continuous time, for infinite, locally finite, connected graphs. For general graphs, a…

We introduce a numerical method for approximating arbitrary differential operators on vector fields in the weak form given point cloud data sampled randomly from a $d$ dimensional manifold embedded in $\mathbb{R}^n$. This method generalizes…

This paper is intended as an introductory survey of a newly emerging field: a topological approach to the study of locally finite graphs that crucially incorporates their ends. Topological arcs and circles, which may pass through ends,…

This paper considers the initial-boundary value problem for the heat equation with a dynamic type boundary condition. Under some regularity, consistency and orthogonality conditions, the existence, uniqueness and continuous dependence upon…

We establish new quantitative estimates for localized finite differences of solutions to the Poisson problem for the fractional Laplace operator with homogeneous Dirichlet conditions of solid type settled in bounded domains satisfying the…