Note on an eigenvalue problem with applications to a Minkowski type regularity problem in Rn

Murat Akman, John Lewis, Andrew Vogel

Research output: Contribution to journalArticle

Abstract

We consider existence and uniqueness of homogeneous solutions u> 0 to certain PDE of p-Laplace type, p fixed, n- 1 < p< ∞, n≥ 2 , when u is a solution in K(α) ⊂ Rn where K(α):={x=(x1,⋯,xn):x1>cosα|x|}forfixedα∈(0,π],with continuous boundary value zero on ∂K(α) \ { 0 }. In our main result we show that if u has continuous boundary value 0 on ∂K(π) then u is homogeneous of degree 1 - (n- 1) / p when p> n- 1. Applications of this result are given to a Minkowski type regularity problem in Rn when n= 2 , 3.

Original languageEnglish (US)
Article number47
JournalCalculus of Variations and Partial Differential Equations
Volume59
Issue number2
DOIs
StatePublished - Apr 1 2020

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Note on an eigenvalue problem with applications to a Minkowski type regularity problem in R<sup>n</sup>'. Together they form a unique fingerprint.

  • Cite this