Note on an eigenvalue problem for an ode originating from a homogeneous p-harmonic function

M. Akman, J. Lewis, A. Vogel

Research output: Contribution to journalArticlepeer-review

Abstract

Abstract. We discuss what is known about homogeneous solutions u to the p-Laplace equation, p fixed, 1 < p < ∞, when (A)u is an entire p-harmonic function on the Euclidean n-space, ℝn, or (B)u > 0 is p-harmonic in the cone with continuous boundary value zero on ∂K(α) \ [0] when α ∈ (0, ϕ]. We also outline a proof of our new result concerning the exact value, λ = 1-(n-1)/p, for an eigenvalue problem in an ODE associated with u when u is p harmonic in K(π) and p > n-1. Generalizations of this result are stated. Our result complements the work of Krol'-Maz'ya for 1 < p ≤ n-1.

Original languageEnglish (US)
Pages (from-to)241-250
Number of pages10
JournalSt. Petersburg Mathematical Journal
Volume31
Issue number2
DOIs
StatePublished - 2020

Keywords

  • Boundary harnack inequalities
  • Eigenvalue problem
  • Homogeneous p-harmonic functions
  • p-Laplacian

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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