This work is concerned with the gradient flow of absolutely p-homogeneous convex
functionals on a Hilbert space, which we show to exhibit finite (p< 2 p< 2) or infinite …

Two key ideas have greatly improved techniques for image enhancement and denoising:
the lifting of image data to multi-orientation distributions and the application of nonlinear …

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

The p-Laplacian is a non-linear generalization of the Laplace operator. In the graph context,
its eigenfunctions are used for data clustering, spectral graph theory, dimensionality …

Extracting the latent underlying structures of complex nonlinear local and nonlocal flows is
essential for their analysis and modeling. In this Element the authors attempt to provide a …

Assignment flows are smooth dynamical systems for data labeling on graphs. Although they
exhibit structural similarities with the well-studied class of replicator dynamics, it is nontrivial …

Extracting the latent underlying structures of complex nonlinear local and nonlocal flows is
essential for their analysis and modeling. In this work, we attempt to provide a consistent …

We address the problem of computing the graph $ p $-Laplacian eigenpairs for $ p\in
(2,\infty) $. We propose a reformulation of the graph $ p $-Laplacian eigenvalue problem in …

Neural networks have revolutionized the field of data science, yielding remarkable solutions
in a data-driven manner. For instance, in the field of mathematical imaging, they have …

In this work, we present an alternative formulation of the higher eigenvalue problem
associated to the infinity Laplacian, which opens the door for numerical approximation of …