Characterization of a homogeneous Orlicz space
Date
2017-02-16
Authors
Arriagada, Waldo
Huentutripay, Jorge
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article we define and characterize the homogeneous Orlicz space Do1,Φ(ℝN) where Φ : ℝ → [0, +∞) is the N-function generated by an odd, increasing and not-necessarily differentiable homeomorphism φ : ℝ → ℝ. The properties of Do1,Φ(ℝN) are treated in connection with the φ-Laplacian eigenvalue problem
-div (φ(|∇u| ∇u/|∇u|) = λ g(⋅)φ(u) in ℝN
where λ ∈ ℝ and g : ℝN → ℝ is measurable. We use a classic Lagrange rule to prove that solutions of the φ-Laplace operator exist and are non-negative.
Description
Keywords
homogeneous space, Orlicz space, eigenvalue problem, phi-Laplacian
Citation
Arriagada, W., & Huentutripay, J. (2017). Characterization of a homogeneous Orlicz space. <i>Electronic Journal of Differential Equations, 2017</i>(49), pp. 1-17.
Rights
Attribution 4.0 International