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 …

We study vector-valued functions that minimise the L∞-norm of their derivatives for
prescribed boundary data. We construct a vector-valued, mass minimising 1-current (ie, a …

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 …

On a general open set of the euclidean space, we study the relation between the embedding
of the homogeneous Sobolev space D 0 1, p into L q and the summability properties of the …

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 …

In this paper we show that if the supremal functional F (V, B)=\rm ess sup x ∈ B f (x, DV (x)) F
(V, B)= ess sup x∈ B f (x, DV (x)) is sequentially weak* lower semicontinuous on W^ 1, ∞ (B …

We study the Γ-convergence of the functionals F n (u):=|| f (⋅, u (⋅), D u (⋅))|| pn (⋅) and F n
(u):=∫ Ω 1 pn (x) fpn (x)(x, u (x), D u (x)) dx defined on X∈{L 1 (Ω, R d), L∞(Ω, R d), C (Ω, R …

We study the limit as p goes to infinity of the first non-zero eigenvalue λp of the p-Laplacian
with Neumann boundary conditions in a smooth bounded domain U of Rn. We prove that …

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 …

We study minimisation problems in L∞ for general quasiconvex first order functionals,
where the class of admissible mappings is constrained by the sublevel sets of another …