We study the non-local eigenvalue problem 2\, ∫\limits _ R^ n| u (y)-u (x)|^ p-2\bigl (u (y)-u
(x)\bigr)| yx|^ α p\, dy+ λ| u (x)|^ p-2 u (x)= 0 for large values of p and derive the limit equation …

A system of local/nonlocal p-Laplacians: The eigenvalue problem and its asymptotic limit as
p→∞ - IOS Press You are viewing a javascript disabled version of the site. Please enable …

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 …

The $ p $-Laplacian operator $\Delta_pu={\rm div}\left (|\nabla u|^{p-2}\nabla u\right) $ is not
uniformly elliptic for any $ p\in (1, 2)\cup (2,\infty) $ and degenerates even more when …

A highly nonlinear eigenvalue problem is studied in a Sobolev space with variable
exponent. The Euler–Lagrange equation for the minimization of a Rayleigh quotient of two …

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

Abstract Let Ω⋐ R n, f∈ C 1 (RN× n) and g∈ C 1 (RN), where N, n∈ N. We study the
minimisation problem of finding u∈ W 0 1,∞(Ω; RN) that satisfies‖ f (D u)‖ L∞(Ω)= inf {‖ f …

This article is concerned with the Dirichlet eigenvalue problem associated with the∞-
Laplacian in metric spaces. We establish a direct partial differential equation approach to …

This paper proves comparison principles for elliptic PDE involving the Finsler infinity
Laplacian, a second-order differential operator with discontinuities in the gradient variable …

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 …