The present article is devoted to present a new characterization of the Cartan isoparametric hypersurfaces in terms of properties of the polynomial, that determines the algebraic set of planar normal sections on the ...

We study a singularly perturbed problem related to infinity Laplacian operator with prescribed boundary values in a region. We prove that solutions are locally (uniformly) Lipschitz continuous, they grow as a linear function, ...

In this note we study the limit as p(x) → ∞ of solutions to −∆p(x)u = 0 in a domain Ω, with Dirichlet boundary conditions. Our approach consists in considering sequences of variable exponents converging uniformly to +∞ and ...

In this paper, we study the behavior as p→ ∞ of eigenvalues and eigenfunctions of a system of p-Laplacians, that is (Formula presented.) in a bounded smooth domain Ω. Here α+ β= p. We assume that α/p→Γ and β/p→1-Γ as p→ ∞ ...

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 λ∞:=lim λp1/p=2/diam(U), where diam(U) ...

Given g an α-H¨older continuous function defined on the boundary of a bounded domain Ω and given ψ a continuous obstacle defined in Ω, in this article, we find u an α-H¨older extension of g in Ω with u ≥ ψ. This function ...

In this work we study the asymptotic behavior of the first non-zero Neumann p-fractional eigenvalue λ1(s,p) as s → 1- and as p → ∞. We show that there exists a constant K such that K(1-s)λ1(s,p) goes to the first non-zero ...

This paper concerns the study of the asymptotic behavior of the solutions to a family of fractional type problems on a bounded domain, satisfying homogeneous Dirichlet boundary conditions. The family of differential operators ...

We characterize p-harmonic functions in terms of an asymptotic mean value property. A p-harmonic function u is a viscosity solution to ∆pu = div(|∇u| p−2∇u) = 0 with 1 < p ≤ ∞ in a domain Ω if and only if the expansion ...

In this article we prove that the first eigenvalue of the ∞− Laplacian { min {− ∆ ∞ v, |∇ v |− λ 1 , ∞ (Ω) v } = 0 in Ω v = 0 on ∂ Ω , has a unique (up to scalar multiplication) maximal solution. This maximal solution can ...