The first eigenvalue of p-Laplacian and geometric estimates
نویسندگان
چکیده
منابع مشابه
The ∞−Laplacian first eigenvalue problem
We review some results about the first eigenvalue of the infinity Laplacian operator and its first eigenfunctions in a general norm context. Those results are obtained in collaboration with several authors: V. Ferone, P. Juutinen and B. Kawohl (see [BFK], [BK1], [BJK] and [BK2]). In section 5 we make some remarks on the simplicity of the first eigenvalue of ∆∞: this will be the object of a join...
متن کاملISOLATION AND SIMPLICITY FOR THE FIRST EIGENVALUE OF THE p-LAPLACIAN WITH A NONLINEAR BOUNDARY CONDITION
Here Ω is a bounded domain in RN with smooth boundary, ∆pu = div(|∇u|p−2∇u) is the p-Laplacian, and ∂/∂ν is the outer normal derivative. In the linear case, that is for p = 2, this eigenvalue problem is known as the Steklov problem (see [3]). Problems of the form (1.1) appear in a natural way when one considers the Sobolev trace inequality. In fact, the immersionW1,p(Ω) ↪→ Lp(∂Ω) is compact, he...
متن کاملSIMPLICITY AND STABILITY OF THE FIRST EIGENVALUE OF A (p; q) LAPLACIAN SYSTEM
This article concerns special properties of the principal eigenvalue of a nonlinear elliptic system with Dirichlet boundary conditions. In particular, we show the simplicity of the first eigenvalue of −∆pu = λ|u|α−1|v|β−1v in Ω, −∆qv = λ|u|α−1|v|β−1u in Ω, (u, v) ∈W 1,p 0 (Ω)×W 1,q 0 (Ω), with respect to the exponents p and q, where Ω is a bounded domain in RN . 1. Preliminaries Eigenvalue prob...
متن کاملEIGENVALUE PROBLEMS WITH p-LAPLACIAN OPERATORS
In this article, we study eigenvalue problems with the p-Laplacian operator: −(|y′|p−2y′)′ = (p− 1)(λρ(x)− q(x))|y|p−2y on (0, πp), where p > 1 and πp ≡ 2π/(p sin(π/p)). We show that if ρ ≡ 1 and q is singlewell with transition point a = πp/2, then the second Neumann eigenvalue is greater than or equal to the first Dirichlet eigenvalue; the equality holds if and only if q is constant. The same ...
متن کاملShape Derivative of the First Eigenvalue of the 1-laplacian
where Ḣ 1 (Ω) is the closure of C ∞ 0 (Ω) in the Sobolev space H 1 1 (Ω) of functions in L(Ω) with one derivative in L. The purpose of this paper is the study of the dependence of λ1,Ω under regular perturbations by diffeomorphisms of Ω, i.e. we want to compute the first variation, the so-called shape derivative, of the functional Ω → λ1,Ω. General results about the stability of λ1,Ω under pert...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nonlinear Analysis and Differential Equations
سال: 2014
ISSN: 1314-7587
DOI: 10.12988/nade.2014.455