Characterization of a homogeneous Orlicz space
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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.
CitationArriagada, W., & Huentutripay, J. (2017). Characterization of a homogeneous Orlicz space. Electronic Journal of Differential Equations, 2017(49), pp. 1-17.
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