Nonlocal $p$-Laplacian Evolution Problems on Graphs

The Nonlocal p-Laplacian Evolution for Image Interpolation

This paper presents an image interpolation model with nonlocal p-Laplacian regularization. The nonlocal p-Laplacian regularization overcomes the drawback of the partial differential equation PDE proposed by Belahmidi and Guichard 2004 that image density diffuses in the directions pointed by local gradient. The grey values of images diffuse along image feature direction not gradient direction un...

The p-median and p-center Problems on Bipartite Graphs

Let $G$ be a bipartite graph. In this paper we consider the two kind of location problems namely $p$-center and $p$-median problems on bipartite graphs. The $p$-center and $p$-median problems asks to find a subset of vertices of cardinality $p$, so that respectively the maximum and sum of the distances from this set to all other vertices in $G$ is minimized. For each case we present some proper...

THE LIMIT AS p →∞ IN A NONLOCAL p−LAPLACIAN EVOLUTION EQUATION. A NONLOCAL APPROXIMATION OF A MODEL FOR SANDPILES

In this paper we study the nonlocal ∞−Laplacian type diffusion equation obtained as the limit as p →∞ to the nonlocal analogous to the p−Laplacian evolution, ut(t, x) = ∫ RN J(x− y)|u(t, y)− u(t, x)|p−2(u(t, y)− u(t, x)) dy. We prove existence and uniqueness of a limit solution that verifies an equation governed by the subdifferetial of a convex energy functional associated to the indicator fun...

On the Nonhomogeneous Fourth-Order p-Laplacian Generalized Sturm-Liouville Nonlocal Boundary Value Problems

Existence results for a class of nonlocal problems involving p-Laplacian

where Ω is a smooth bounded domain in R, 1 0, such that (M0) M(t) ≥ m0 for all t ≥ 0. f (x, t) : × R → R is a continuous function and satisfies the subcritical condition: ∣∣f (x, t)∣∣ ≤ C(|t|q−1 + 1), for some p < q ...