Tackling semi-supervised learning problems with graph-based methods has become a trend
in recent years since graphs can represent all kinds of data and provide a suitable …

In this article we characterize the $\mathrm {L}^\infty $ eigenvalue problem associated to the
Rayleigh quotient $\left.{\|\nabla u\| _ {\mathrm {L}^\infty}}\middle/{\| u\| _\infty}\right. $ and …

Cheeger's inequality states that a tightly connected subset can be extracted from a graph G
using an eigenvector of the normalized Laplacian associated with G. More specifically, we …

We study the Neumann and Dirichlet problems for the total variation flow in doubling metric
measure spaces supporting a weak Poincaré inequality. We prove existence and …

Landscape functions are a popular tool used to provide upper bounds for eigenvectors of
Schrödinger operators on domains. We review some known results obtained in the last 10 …

The p-Laplacian evolution equation in metric measure spaces has been studied as the
gradient flow in L 2 of the p-Cheeger energy (for 1< p<∞). In this paper, using the first-order …

The aim of this paper is to revisit the definition of differential operators on hypergraphs,
which are a natural extension of graphs in systems based on interactions beyond pairs. In …

In this work we develop a nonlinear decomposition, associated with nonlinear
eigenfunctions of the p-Laplacian for p∈(1, 2). With this decomposition we can process …

Our aim is to study the Total Variation Flow in Metric Graphs. First, we define the functions of
bounded variation in Metric Graphs and their total variation, we also give an integration by …

We analyse the functional 𝒥 (u)=∥∇ u∥∞ defined on Lipschitz functions with
homogeneous Dirichlet boundary conditions. Our analysis is performed directly on the …